Ishwar is Saguna Brahman who has created the world out of Maya according to Advait Vedanta. Although Ishwar too is illusion according to it, who is Ishwar actually - Lord Shiva or Vishnu as both can not be Ishwar of same creation. Or none of them is Ishwar?
Note: whenever Advait of Lord Vishnu or Shiva is established, it is established as Nirguna Brahman only. I want clear explanation on the level of Ishwar or Saguna Brahman as there can not be 2 Ishwar.
Pure Advaita considers forms of God as unreal. Thus it does not matter what name the unreal Ishvara is called.
Shankara considers Isvara or Brahman with attributes as ultimately unreal. He writes in his commentary on Brahma Sutra Bhasya:
Since this Self is by nature Consciousness Itself, distinctionless, beyond speech and mind, and can be taught by way of negating other things, hence in the scriptures dealing with liberation an illustration is cited by saying that it is "like the sun reflected in water". Here the aspect kept in view is the one with attributes, which is not real and which is created by limiting adjuncts, as it is done in such texts, "As this luminous sun, though one in itself, becomes multifarious owing to its entry into water divided by different pots, similarly this Deity, the birthless, self-effulgent Self, though one, seems to be diversified owing to its entry into the different bodies, constituting its limiting adjuncts." Similarly, 'Being but one, the Universal Soul is present in all beings, though One, It is seen as many, like the moon in water" (Amritabindu, 12) and other texts.
Brahma Sutra Bhasya of Sri Sankaracharya, III.II.18
According to Sarva Vedanta Siddhanta Saara Sangraha (You can get Sanskti-Hindi version from Internet Archive).
verses 310-317 Ishvara ॥ १४ ॥ ईश्वरः॥
मायोपहितचैतन्यं साभासं सत्त्वबृंहितम् । सर्वज्ञत्वादिगुणकं सृष्टिस्थित्यन्तकारणम् ॥ ३१०॥
अव्याकृतं तदव्यक्तमीश इत्यपि गीयते । सर्वशक्तिगुणोपेतः सर्वज्ञानावभासकः ॥ ३११॥
स्वतन्त्रः सत्यसङ्कल्पः सत्यकामः स ईश्वरः । तस्यैतस्य महाविष्णोर्महाशक्तेर्महीयसः ॥ ३१२॥
सर्वज्ञत्वेश्वरत्वादिकारणत्वान्मनीषिणः । कारणं वपुरित्याहुः समष्टिं सत्त्वबृंहितम् ॥ ३१३॥
आनन्दप्रचुरत्वेन छादकत्वेन कोशवत् । सैषानन्दमयः कोश इतीशस्य निगद्यते ॥ ३१४॥
सर्वोपरमहेतुत्वात्सुषुप्तिस्थानमिष्यते । प्राकृतः प्रलयो यत्र श्राव्यते श्रुतिभिर्मुहुः ॥ ३१५॥
अज्ञानं व्यष्ट्यभिप्रायादनेकत्वेन भिद्यते । अज्ञानवृत्तयो नाना तत्तद्गुणविलक्षणाः ॥ ३१६॥
वनस्य व्यष्ट्यभिप्रायाद्भूरुहा इत्यनेकता । यथा तथैवाज्ञानस्य व्यष्टितः स्यादनेकता ॥ ३१७॥
Note:Adding English translation
According to Shata Sloki of Adi Shankaracharya,
6. This Maya has four great qualities. It is ever youthful and ever new. It has the capacity to make what is impossible happen. Every action undertaken as a result of this Maya is sweet in the beginning. Maya conceals the knowledge about Brahman contained in the Srutis. Isvara and Jiva both dwell in this Maya like two birds on a tree. The Jiva experiences external objects through the sense organs and feels happiness or misery, while Isvara is not affected by them.
This verse is based on the Rigveda, 8.6.16.3. There Maya is described as a girl having the above four qualities. Maya has two powers, the veiling power (Avarana sakti) and the projecting power (Vikshepa sakti). Maya veils Brahman and projects the universe. It thus makes the impossible happen. Brahman reflected in pure (Sattvic) Maya is Isvara (God). The Jiva or individual is Brahman reflected in Avidya, which is impure Maya because of the admixture of Rajoguna and Tamoguna. It is therefore stated in this verse that both Isvara and Jiva dwell in Maya. The comparison with two birds on the same tree is based on Mundakopanishad, III.i.1, which says: - "Two birds that are ever associated with each other reside on the same tree (standing for the body). One of them, (the Jiva), eats the fruits (i.e. experiences the results, good and bad, of its karma) because of identification with the body. The other, Isvara, looks on without eating. Isvara has no karma to be experienced and no identification with the body. Isvara controls Maya, while the Jiva is under the control of Maya.
All actions undertaken are sweet in the beginning - The Jiva undertakes various actions with the object of attaining happiness, prompted by Maya or ignorance of the truth that he is Brahman. He feels happy when he starts such action, only to realize ultimately that all such actions ultimately lead only to sorrow, because nothing obtained by action can give everlasting happiness. Only the realization that one is in reality Brahman will give eternal happiness unmixed with the slightest trace of misery. This knowledge, which is contained in the Upanishads, is concealed by ignorance and so the Jiva looks upon himself as a limited individual. See Gita, 5.16.
Maya makes the impossible happen - Sri Sankara gives, in Mayapanchakam, some instances of this. It imposes on Brahman, which is eternal and devoid of parts and which is pure Consciousness, the false distinctions as the world, individual souls and God. It makes even those who have mastered all the scriptures no different from animals by tempting them with wealth and the like. It makes Brahman which is infinite bliss, pure consciousness and non-dual, struggle in the ocean of samsaara by associating it with the body made up of the five elements. It imposes on Brahman which is devoid of qualities, the distinctions of colour, caste, etc, and attachment to wife, son, possessions and the like. It creates even in non-dual Brahman distinctions such as Brahmaa, Vishnu and Siva and deludes even the learned into thinking that they are different from one another.
Note.
Yeah, there can be only one Saguna Brahman as the following verse maintains-
B.Su. 4,4.17. (The released soul attains all lordly powers) except the power of creation etc., on account of (Iswara being) the subject-matter (of all texts where creation etc. are described), and (the released souls) not being mentioned (in that connection)...Moreover, this would lead to many Iswaras, which may give rise to a conflict of wills with respect to creation etc. Therefore the powers of the liberated souls are not absolute but limited, and are dependent on the will of Iswara.
But it seems Saguna Brahman of Shankara Vedanta is distributed in nature rather than a centralized one.
B.Su 4.3.8...“And conducts them to the worlds of Brahman” (Brih. 6. 2. 15). The plural number is not possible with respect to the Supreme Brahman, while it is possible in the case of the Saguna Brahman, which may abide in different conditions.
So when Saguna Brahman is distributed in nature, it can simultaneously be present as various forms like of Vishnu, Shiva, Brahma, etc. Therefore, all can be different manifestations of the same Saguna Brahman parallely. Let me end the answer with a verse of Maya Panchakam by Adi Shankara.
विधिहरिहरविभेदमप्यखण्डे
बत विरचय्य बुधानपि प्रकामम् ।
भ्रमयति हरिहरभेदभावा-
नघटितघटनापटीयसी माया ॥ ५॥
5. Alas! Maya, which is adept at making the impossible happen, creates in Brahman which is homogeneous, without any parts, distinctions such as Brahma, Vishnu and Siva and thereby perplexes even the learned by making them look upon Brahma, Vishnu, and Siva as different from one another.
If God is Moon than Shiva and Vishnu are like craters on that Moon. God has no name
The following verses from the Upanishads refer to the Concept of God:
Ekam evadvitiyam
Meaning: He is One only without a second. [Chandogya Upanishad 6:2:1]Na casya kascij janita na cadhipah
Meaning: Of Him there are neither parents nor lord.[Svetasvatara Upanishad 6:9]
Na tasya pratima asti
Meaning: There is no likeness of Him. [Svetasvatara Upanishad 4:19]
The following verses from the Upanishad allude to the inability of man to imagine God in a particular form:
Na samdrse tisthati rupam asya, na caksusa pasyati kas canainam. Meaning: His form is not to be seen; no one sees Him with the eye. [Svetasvatara Upanishad 4:20]
He has no form as explained in Vedas like Yajurveda:
na tasya pratima asti
Meaning: There is no image of Him.
[Yajurveda 32:3]shudhama poapvidham
Meaning: He is bodyless and pure.
[Yajurveda 40:8]
Brahma Sutra of Hinduism:
Ekam Brahm, dvitiya naste neh na naste kinchan Meaning: There is only one God, not the second; not at all, not at all, not in the least bit.
Shiva is a collection of 11 Rudras described in Vedas/Upanishads while Vishnu is collection of 8 Vasus, further Surya/Sun God is worshipped with Gayatri and is collection of 12 Adityas. +1 Indra and +1 Brahma are total 33 koti devtas.
Puranas are Smritis that were created for Shudras and Women who had low intellect to understand reality, but Vedas are Shrutis and are highest-eternal to be studied by only Brahmins and learned Kshatriyas.
What is difference between Shruti and Smriti?
Between Smritis and Shrutis, Shrutis always speaks the truth https://en.wikipedia.org/wiki/Aham_Brahmasmi
स्वतः पूर्णः परात्माऽत्र ब्रह्मशब्देन वर्णितः | अस्मीत्यैक्य-परामर्शः तेन ब्रह्म भवाम्यहम् ||
Meaning: Infinite by nature, the Supreme Self is described here by the word Brahman (lit. ever expanding; the ultimate reality); the word asmi denotes the identity of aham and Brahman. Therefore, (the meaning of the expression is) "I am Brahman."
Aham Brahmasmi is the core of whole Vedas that is key for Kaivalya Moksha and leads to Sat Chida Ananda
Even Rama says so:-
I-i-15-17. Hanuman: Rama, sages speak differently: some say there is only one kind of liberation. Others say it can be got by worshipping your name and by the Taraka mantra at Kashi. Others speak of Sankhya-Yoga and Bhakti-Yoga, the enquiry into Vedanta-Vakyas etc.
I-i-18-23. Rama: Liberation is of four kinds: Salokya, Sameepya, etc. But the only real type is Kaivalya. Others are waste of human life.
The SAME Paramatman (Saguna Brahman) is called as (acknowledged as) Brahma, Vishnu or Shiva depending on the context. Just like the same person in the world can be a Father, Son, Husband etc..depending on who is addressing him.
