Is there any relation or similarity between Rudra & Indra?

Question

According to Tejaswee's Answer on What is the Vedic Origin of Lord Shiva?:

Similarly, Indra is also a manifestation of Lord Rudra. AtharvaVeda calls Rudra as slayer of Vritta which is actually Indra:

“sahasrākṣáu vr̥trahánā huveháṃ dūrégavyūtī stuvánn my ugráu |
yā́v asyéśathe dvipádo yáu cátuṣpadas táu no muñcatam áṃhasaḥ ||” (Atharvaveda 4:28:03)

“The thousand-eyed slayers of Vritra both do I invoke. I go praising the two strong gods (ugrau) whose pastures extend far. Ye who rule all these two-footed and four-footed creatures [Pasupati], deliver us from grief and trouble”.

YajurVeda which states everything like fire, water, air, sun, moon, etc... gained their characteristics features because Lord Shiva manifested as Ashtamurti Rupa ie. He entered in all those 8 things as Purusha and made them active. Satapatha Brahmana of YajurVeda from 6.1.3.10 to 6.1.3.17 states:

Rudra is Agni.
Sarva is Water (Varuna).
Pasupati is Plants (Vanaspati).
Ugra is Air (Vayu).
Asani is Lightening.
Bhava is Raingod (Parjanya).
Mahadeva is Moon (Chandra/Soma/Mind).
Ishana is Sun (Surya/ Atman)

Thus, it is clear the whole world is pervaded by the forms of Lord Rudra. So as Rudra is actually Agni, Vayu, Varuna, Soma, Surya, etc.. as seen from above Shruti passage (of YajurVeda). So actually Vedic hymns to all these Gods are actually praying various forms and manifestations of Lord Rudra.

According to Rig Veda 2:33:03:

“śreṣṭho jātasya rudra śriyāsi tavastamastavasāṃ vajrabāho |
parṣi ṇaḥ pāramaṃhasaḥ svasti viśvā abhītī rapaso yuyodhi ||” (Rig Veda 2:33:03)

“In beauty thou art the most beautiful of all that exists, O Rudra, the strongest of the strong, thou wielder of the thunderbolt! Carry us happily to the other shore of our anguish, and ward off all assaults of mischief”.

^{Source: Glory of Lord Kameshwara- VI: Kama Sukta - India Facts}

I have read about Rudra being described as vajrabaahu(holder of thunderbolt), asani (lightening or vidyut) or meghapati (master of clouds). How can this be briefly explained?

Answer 1

Rig Vedic seers realised through deep meditation that the same formless Almighty God, appears to us in the form of the NATURE, which gives sustenance to all beings.

Sri Krishna said;

पिताऽहमस्य जगतो माता धाता पितामहः।

वेद्यं पवित्रमोंकार ऋक् साम यजुरेव च।।9.17।।

Of this world I am the father, mother, ordainer, (and the), grand-father; I am the knowable, the sancitifier, the syllable Om as also Rk, Sama and Yajus.

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Again, the NATURE will provide land for cultivation of crops, provide material for construction of shelters for protecting ourselves, provide fire for cooking or burning something, etc, provide water and air for carrying out many activities, etc.

So the NATURE, the visible face of the invisible GOD, was understood and worshipped by the Rig Vedic seers.

In Rig Veda, the Almighty God was described in different names like Indra, Agni, Vayu, Vishnu, etc, according to the form, the Almighty's power was perceived.

This is one side of the coin,ie., one face of the God.

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However, the same NATURE make us cry, fear, shout, feel ashamed, feel jealous of someone, etc.

This is another side of the God.

The seers called this form of the God as Rudra.

The seers described the God in the form of Rudra as taskaranam pataye - Lord of thieves, in Sri Rudram.

Namo nishangina ishudhimate taskaranam pataye namo |

What does the God steal from us?

The God steals, the power to think, act properly,etc, when humans indulge in indriyAs (senses). The more we get indulged in indriyAs (senses), greater will be suffering, and happiness will be lost. Thus, the epithet Rudra refers to the Almighty God, the Lord of indriyAs.

When indriyAs (senses) were brought under control and the ABSOLUTE BLISS has been attained, we will be protected from suffering. And, thus he is Indra, as the saviour. That is why he was described as wielder of the thunderbolt , on indriyAs (senses), in Rig Veda 2:33:03.

So the God is described as Rudra as well as Indra.

The vedas also describe Rudra as Sovereign of this world (RV 2.33.9)

sthirebhiraṅghaiḥ pururūpa ughro babhruḥ śukrebhiḥ pipiśehiraṇyaiḥ īśānādasya bhuvanasya bhūrerna vā u yoṣad rudrādasuryam (RV 2.33.9)

With firm limbs, multiform, the strong, the tawny adorns himself with bright gold decorations: The strength of Godhead never departs from Rudra, him who is Sovereign of this world, the mighty.

Answer 2

Preface: Before we describe the relationship or contrast between Rudra and Indra, one has to understand that Vedas describe both Divinities (Devas) and Divine-Concepts (All encompassing Deva). Divine Concepts are like Soma, Rudra, Indra, Prajapati, Purusha, Vrātyas, Manyu and more. These Divine Concepts are not individual divinities limited to a Yajna or a single event, they are omniscient concepts that overlap with other Divinities. In the end, they are all cumulative of Rta.

Highnote: Rudra is a RAW Concept, meaning one can't just limit Rudra = 'XYZ' and be done with it, doing so is a half-baked attempt. The concept of Rudra overlaps with various Devas (divinities) Like Soma, Agni, Vayu... This is why Vedas were very very specific in addressing Rudra as:

1. Viṣvarūpam = meaning the cosmic form or the all-encompassing omni-form
2. Pururūpam = meaning multiform/multihued, and
3. Virūpam = meaning multifold altering forms and
4. Vahurūpa = meaning multi-formed (References RV2.33.10,TS4.5.4,TA10.23.1)

The details in which Rudra is explained in the Vedas are astonishing, so are Soma, Prajapati, and Indra more than any.

Rudra vs Indra : Source: LINK

1. Rudras (rudrébhis or rudrésu) are the only Divinities in the Vedas to possess a multitude of precise and powerful weapons. Atharva Veda speaks of Rudra's golden bows and weapons flying abroad like guided missiles in the direction he desires AV11.2.12. The only other Divinity who comes close to possessing multiple weapons is Indra; He too has a weapon common to Rudra, which is the lightning (Asani). These hymns define Rudras and Maruts as Earth-shaking clans feared by all lokas as they could create fires, bring rain (nourishment and lords of food RV2.1.6), hunts like predators, and attacks in thousands, and kill in hundreds AV11.2.12 causes lightning and thunder [RV1.38,2.33,5.58/59, KYV4.5.11, AV11.2.26], and make rain in deserts RV1.38.7. Hence he is called the Tempest God, and also has the title Aśani given to Rudra in Brahmāṇa-1 of Vājasaneyi Saṃhitā 8.1.3.6.
2. In numerous hymns, Agni, Indra, Atithi, and others are urged to pass on their recommendations and pleas to Rudras/Maruts through Rudriya & Marutvatia (hymns dedicated to Rudra/Maruts respectively). On many occasions, various Divinities request the help of Rudras/Maruts as their strength is invincible in battle RV1:87,167. Indra will not overwrite the boons given by Maruts RV1:166 as they are his trusted friends and comrades AB1.3.20. There is a story in the Puráńas of how Viṣṇu led Maruts to a battle. Viṣṇu is also called Evaya Marut, meaning the fastest Marut RV5.87 and the title ŚipiViṣṭa (शिपिविष्ट) RV7.100.6 meaning the rays which permeate, this title is given to both Viṣṇu and Rudra TS4.5.5. Aitareya Brahmāṇa 1.30 states that Viṣṇu is the leader of the Maruts and both Ashivns and Varuna who themselves being Rudras follow His lead. The twin Ashvins are also considered as Rudras - "उत नो॑ रुद्रा चिन्मृळतामश्विना" RV10.93.7 and they move like the Rudra, hence the word Rudravartanī (रुद्रवर्तनी) which means to move forwards boldly/fiercely with brilliance like Rudra RV1.3.3. It's because of this hymn many observed a commonality among the twin Ashvins with that of Rudras, and the most obvious trait of them being Physicians just like Rudra. Hence are considered as the children of Rudra. As Sri Aurobindo famously says, if Viṣṇu is the all-encompassing space/canvas, and Brahma is the Creative Idea, Rudra is the invisible force that propels Creation forward to the highest state/stride of Viṣṇu and bestows bliss/nourishment RV1.114 in their journey. When we say nature.
3. Rudra is not necessarily a single entity or a group because of the unique nature of Rudra to manifest across various concepts and divinities. So Rudra is a polar divinity, unlike Indra. Since Rudra is the raw and un-manifested invisible force, with the knowledge and immortal wisdom came the Maruts as the individual forces of nature wielded by Rudra. These forces cause the evolution of creation and favorite to Indra in the destruction of VritraAB3.20. THE RUDRA is not as a person but as "The Concept of Sovereignty and All-Encompassing Cosmic form" Hence, Rudras can save us, at the same time, cause destruction to restructure things in Creation, this is why Rudras are all-encompassing form and are not limited to fixed attributes/actions and the Maruts are called the arrows/missiles of Rudra.
4. Source: LINK The most distinctive attribute of Rudra is His long hair, Vedas gave three distinctive titles, they said Harikeśa (हरिकेशेभ्य) YV4.5.2 MB1.17.11 and Vyuptakeśa (व्युप्तकेश) and Kaparddi (कपर्दिने) YV4.5.5. Harikeśa has many meanings, like self-Luminant, golden-head/hair, or fair-headed which means the one who is unprejudiced towards all beings. The most interesting part is that Indra is also addressed as Harikeśa RV10.96.5. This title has many compounds (Sandhi) in Sanskrit like Hari+keśa or Hari+ka+iśa. 
5. Source: LINK Similar to Rudra, the concept of Soma enters into various aspects of the Yajñá (Yagna). In this way, Soma enters into the offering of the Soma:latha juice, into clarified butter (ghee) used in Yagna, or the full moon, into medicines, into amṛta, and is the very ṛta. In other places, Somapavamana, meaning the purified/clarified/refined version of Soma, gave rise to both Indra and Viṣṇu during Yajñá RV9.96.5. This does not mean Viṣṇu takes physical birth because various divine concepts (Devas) emerge during various states of Yajñá performed by Prajāpati. Soma is also addressed as an additive to milk or ghee used as Medha (offering) of Yajñá. Soma is also used as a synonym for amṛta and it is this Soma that the Devas compete RV1.108, Indra more than others, as his strength comes from the divine Soma through which He and other Devas conquered all the worlds RV8.92/9.62.29. It is this Soma that gives them health, immortality, and strength to fight off Vṛtra, allowing room for ṛta. To this, the Maruts provide their support. Many dualities are paired among various divine concepts in the Vedas, like Mitra-Varuna, similarly, Rudra and Soma are paired together as a dual divinity across Vedas and are treated as one.
6. Taittirīya Saṃhitā 2.2.11 gives us a brief glimpse into an event where both Ausras and Devas reach a disagreement and when they leave, Soma leaves with Rudras and Agni leaves with Vasus, Indra with Maruts and Varuna with Ādityās.
7. Source: LINK Let's go to Mahabharatam Sauptika Parva, in which Yudhishthira (Dharmaraj), in despair for losing his children and many others to Drona's son Ashwathama questions Śrī Kṛṣṇa (Vasudeva), for which He replies:

The holy one said, 'Verily, Drona's son had sought the aid of that highest of all the gods, viz., the eternal Mahadeva. It was for this that he succeeded in slaying, single-handed, so large a number of warriors. If Mahadeva be gratified, he can bestow even immortality and Girisha can give such valor as will succeed in checking Indra himself. I know Mahadeva truly, O bull of Bharata's race! I know also his various acts of old. He, O Bharata, is the beginning, the middle, and the end of all creatures. The entire Universe acts and moves through his energy.~Mahabharatam Itihāsa Sauptika Parva 17 8. The Atharva Veda points to Indra's role as the supreme ruler in terms of the administration of Creation and Yajñá, but there is no clear reference of him being addressed as one of the Rudras. However, both Rudra and Indra share many similar titles like Vāstoṣpati, Vrittahan, Bhutapati & Satpatim. Asani is an epithet of Rudra in the form of a thunderbolt held by Indra which is also mentioned in Mahābhāratam. 9. Let's go to Caraka Katha Āraṇyaka 2.100/101 Wandering Rudra in the heavenly realm (svargaṃ lokaṃ) with a sun-like luster/brilliance (ādityavarṇaṃ). The Devas who ascended to the heavenly realm saw and sought Rudra as to who he was (.abruvan: ko .asīti). I am Rudra (ahaṃ rudro), I am Indra (aham indro), I am the Āditya (aham indro, aham ādityo), I am divine brilliance the encompases entirity ( ahaṃ sarvasyāvayā haraso divyasyeti). The Devas claimed no offering to Rudra. He Roared fiercely towards them (rudratvam). The devas realized this and addressed him with due reverence by calling him Bhava. They said Bhava the entirety is thy Sarva. Because they said you are all this that revealed Śarva’s [prowess] as an archer. Because he then became favorable that is Śiva’s benevolence. ~Caraka Katha Āraṇyaka 2.100/101 10. Vyasa said: 'Hearing these words of the lotus-born Brahma, Maheswara became gratified. Desirous of extending his grace, he laughed aloud. The celestials then gratified (with praise) both Uma and Rudra. The arm of the thunder-wielding Sakra re-got its natural state. That foremost one of all the gods, that destroyer of Daksha's sacrifice, that divine lord having the bull for his sign, became gratified with the gods. He is Rudra he is Siva, he is Agni, he is everything, and he hath knowledge of everything. He is Indra, he is the Wind, he is the twin Aswins, and he is the lighting. He is Bhava, he is Parjanya, he is Mahadeva, he is sinless. He is the Moon, he is Isana, he is Surya, he is Varuna. He is Kala, he is Antaka, he is Mrityu, he is Yama. 1 He is the day, and he is the night. He is the fortnight, he is the month, he is the seasons. He is the morning and evening-twilights, he is the year. He is Dhatri, he is Vidhatri, he is the Soul of the universe, and he is the doer of all acts in the universe. Though himself without body, it is he who is the embodied celestial. ~Mahābhāratam Drona Parva Section 202-203 (jaya section)

 Hope this provides you with what you seek. Pranam