Lord tvastar is an artisan God who is praised In the Vedas and Vishwakarma is also considered An artisan God in puranas and epics. So are these the different names of the same god or are they two different Gods?
There is a lot of confusion regarding these two perhaps because the Puranas mention Vishwakarma as the doer of things that Vedas mention Tavshtar to have done. This book mentions the same:
But there is a huge distinction between Vedic & Puranic Vishwakarma - Vedas use Vishwakarman most often as an adjective not the name of a person. It is an epithet for the Supreme God, like Brahman, since He is the one who creates everything, a job that the Puranas give to Brahma. This is evident from Rig Veda Book 10, Verse 81 which describes Vishwakarman similar to the way the Cosmic Purush is described:
HE who sate down as Hotar-priest, the Ṛṣi, our Father, offering up all things existing,— He, seeking through his wish a great possession, came among men on earth as archetypal.
What was the place whereon he took his station? What was it that supported him? How was it? Whence Visvakarman, seeing all, producing the earth, with mighty power disclosed the heavens.
He who hath eyes on all sides round about him, a mouth on all sides, arms and feet on all sides, He, the Sole God, producing earth and heaven, weldeth them, with his arms as wings, together.
What was the tree, what wood in sooth produced it, from which they fashioned out the earth and heaven? Ye thoughtful men inquire within your spirit whereon he stood when he established all things.
Nine highest, lowest, sacrificial natures, and these thy mid-most here, O Visvakarman, Teach thou thy friends at sacrifice, O Blessed, and come thyself, exalted, to our worship.
Bring thou thyself, exalted with oblation, O Visvakarman, Earth and Heaven to worship. Let other men around us live in folly here let us have a rich and liberal patron.
Let us invoke to-day, to aid our labour, the Lord of Speech, the thought-swift Visvakarman. May he hear kindly all our invocations who gives all bliss for aid, whose works are righteous.
The Next Verse RV.10.82 also strengthens the same belief:
THE Father of the eye, the Wise in spirit, created both these worlds submerged in fatness. Then when the eastern ends were firmly fastened, the heavens and the earth were far extended.
Mighty in mind and power is Visvakarman, Maker, Disposer, and most lofty Presence. Their offerings joy in rich juice where they value One, only One, beyond the Seven Ṛṣis.
Father who made us, he who, as Disposer, knoweth all races and all things existing, Even he alone, the Deities' narne-giver,him other beings seek for information.
To him in sacrifice they offered treasures,—Ṛṣis of old, in numerous troops, as singers, Who, in the distant, near, and lower region, made ready all these things that have existence.
That which is earlier than this earth and heaven, before the Asuras and Gods had being,— What was the germ primeval which the waters received where all the Gods were seen together?
The waters, they received that germ primeval wherein the Gods were gathered all together. It rested set upon the Unborn's navel, that One wherein abide all things existing.
Ye will not find him who produced these creatures: another thing hath risen up among you. Enwrapt in misty cloud, with lips that stammer, hymn-chanters wander and are discontented.
The sixth verse of the above hymn clearly mentions the navel of the unborn Lord who lies in water again hinting that the verse is actually meant for Lord Narayan who creates the world in the form of Brahma. The actual Sanskrit verse in fact mentions as Tvashtar originating from Vishwakarman:
अ॒द्भ्यः सम्भू॑तः पृथि॒व्यै रसा॓च्च । वि॒श्वक॑र्मणः॒ सम॑वर्त॒ताधि॑ । तस्य॒ त्वष्टा॑ वि॒दध॑द्रू॒पमे॑ति । तत्पुरु॑षस्य॒ विश्व॒माजा॑न॒मग्रे॓ ॥
The Vedic Tvashtar on the other hand is considered the artist who creates an embryo inside a woman's womb. Atharva Veda Book 5 Hymn 25 mentions the following:
4-5 Let Mitra-Varuna and God Brihaspati lay the germ in thee. Indra and Agni lay the germ, Dhātar bestow the germ in thee. Let Vishnu form and mould the womb, let Tvashtar duly shape the forms.
11 Tvashtar, celestial artist, lay within the body of this dame. A male germ with the noblest form for her in the tenth month to bear.
Shukla Yajurveda Book 29 Verse 9 mentions something similar:
9 The God-devoted son Tvashtar produces: from Tvashtar springs to life your fleet-foot Courser. Tvashtar gave being to this All about us. Priest, worship here the mighty work's achiever.
He is even invoked in Atharva Veda Wedding Hymn for he created both the male and the female forms:
Tvashtar formed her to be thy dame, Tvashtar made thee to be her lord. Long life let Tvashtar give you both. Let Tvashtar give a thousand lives.
Rig Veda Book 3 Verse 55 also mentions something to that effect:
19 Tvaṣṭar the God, the omniform. Creator, begets and feeds mankind in various manner. His, verily, arc all these living creatures. Great is the Gods’ supreme dominion.
Additionally, the Vedas also make him the father-in-law of Surya. As mentioned in Rig Ved Verse 17.1 of Book 10:
Tvashtar prepares the bridal of his Daughter: all the world hears the tidings and assembles. But Yama's Mother, Spouse of great Vivasvān, vanished as she was carried to her dwelling.
RV Book 10. Verse 10.5 also mentions him as the creator of Yama and Yami, the offspring of Surya and Saranyu referring to his dual role as the fashioner of embryos as well as their forefather:
Even in the womb God Tvaṣṭar, Vivifier, shaping all forms, Creator, made us consorts. None violates his holy ordinances: that we are his the heavens and earth acknowledge.
Tvashtar also sired Trisiras or Vishwaroop as well as created Vritra. His being the father of Trisiras is also mentioned at multiple places one example being:
Well-skilled to use the weapons of his Father, Āptya, urged on by Indra, fought the battle. Then Trita slew the foe seven-rayed, three-headed, and freed the cattle of the Son of Tvaṣṭar.
Lord of the brave, Indra cleft him in pieces who sought to gain much strength and deemed him mighty. He smote his three heads from his body, seizing the cattle of the oniniform (Vishwaroop) Son of Tvaṣṭar.
Paradoxically, he also created the Vajra with which Vritra was slayed as discussed in this question that was answered by you. Now all this is as per the Vedas and we get corroboration of some of this in the Mahabharat. Section 9 of Udyog Parva mentions the relationship between Tvashtar and Trisiras/Viswaroop as well as Vritra:
Once Twashtri the lord of creatures and the foremost of celestials, was engaged in practising rigid austerities. And it is said that from antipathy to Indra he created a son having three heads. And that being of universal form (Viswaroop) possessed of great lustre hankered after Indra's seat.
After Indra kills Vishwaroop the enraged Tvashtar creates Vritra to avenge his son's death and this text does not mention that he created the Vajra:
Now when the lord of creatures, Twashtri, heard that his son had been slain by Indra, his eyes became red with ire, and he spoke the following words, 'Since Indra hath killed my son who had committed no offence at all, who was constantly engaged in the practice of austerities, who was merciful, possessed of self-control, and of subdued passions, therefore, for the destruction of Indra, I will create Vritra.
The Purans however add a different persepective by calling him an Aditya, one of the sons of Aditi. Vishnu Puran Book 1 Chapter 15 mentions the following:
There were twelve celebrated deities in a former Manwantara, called Tushitas, who, upon the approach of the present period, or in the reign of the last Manu, Chákshusha, assembled, and said to one another, "Come, let us quickly enter into the womb of Adití, that we may be born in the next Manwantara, for thereby we shall again enjoy the rank of gods:" and accordingly they were born the sons of Kaśyapa, the son of Maríchi, by Adití, the daughter of Daksha; thence named the twelve Ádityas; whose appellations were respectively, Vishńu, Śakra, Áryaman, Dhútí, Twásht́ri, Púshan, Vivaswat, Savitri, Mitra, Varuńa, Anśa, and Bhaga.
Coming to Vishwakarma in the Purans, the Chapter 25 of Book 1 of Vishnu Purana calls him the son of the Vasu Prabhas and Yogasiddha, the sister of Devguru Brihaspati:
The sister of Váchaspati, lovely and virtuous, Yogasiddhá, who pervades the whole world without being devoted to it, was the wife of Prabhása, the eighth of the Vasus, and bore to him the patriarch Viswakarmá, the author of a thousand arts, the mechanist of the gods, the fabricator of all ornaments, the chief of artists, the constructor of the self-moving chariots of the deities, and by whose skill men obtain subsistence. Ajaikapád, Ahirvradhna, and the wise Rudra Twasht́ri, were born; and the self-born son of Twashtri was also the celebrated Viśwarúpa.
There are thus two different Tvasthars mentioned in the same Puran but the above passage tells us that it was Rudra Tvashtri, the son of Vishwakarma whose son was Trishiras.
Another corroboration of this thought comes from Section 1.3.23 of the Shiva Puran where Vishwakarma is mentioned to have fashioned the Vajra for Indra to kill the demon Vritrasur:
Dadhichi Gave up his life by his yogic power. Indra then instructed Kamdhenu to extract the bones from the dead body of Dadhichi. The bones were on given to 'Twashta' to construct the weapon-Vajra. Twashta took the weapons to Vishwakarma who at last constructed the Vajra.
Thus even in the Puranas Tvashtar and Vishwakarma are different just as they are in Vedas but the Purans confuse the terms when they make the father as the owner of the achievements of his son. This can be again seen in Vishnu Puran Book 3, Chapter 2 that mentions Vishwakarma as the father of Surya's wife:
Sanjná, the daughter of Viśwakarman, was the wife of the sun, and bore him three children, the Manu (Vaivaswata), Yama, and the goddess Yamí (or the Yamuná river).
To sum it up, Vedic Vishwakarman refers to God as the Creator while Vedic Tvashtar refers to the specific artisan known in the Purans as Vishwakarma who is the father-in-law of Surya and also the designer of the Vajra.