According to wikia

". Whether Goratrix knew what would happen is known only by him and, perhaps, Tremere, but at the completion of the ritual the participants fell unconscious and were reborn as vampires, their avatars destroyed and magical abilities lost. The mages had gained their immortality but lost the power they lived for."

[url=http://whitewolf.wikia.com/wiki/Tremere_(VTM]http://whitewolf.wikia.com/wiki/Tremere_(VTM[/url])

"is what allows blood magicians to shape the world without inviting the Paradox that plagues true mages, as they do not rely on external Spheres, but on something that is contained deep within their own essence. Noddists that have knowledge of this claim that this was the reason Caine killed his brother, to invite God's curse upon him to steal a part of His power."

[url=http://whitewolf.wikia.com/wiki/Blood_magic_(VTM]http://whitewolf.wikia.com/wiki/Blood_magic_(VTM[/url])

So apparently the main difference is that Thaumaturgy don't "cause" paradox.

"Paradox can take a variety of forms. Backlash, reality directly attacking the offensive mage, can cause temporary, long term, or even permanent wounds, flaws, or oddities. Quiet, a magical form of madness, forces the offending mage to resolve their guilt over disjointing reality. Exceptionally offensive Mages can be catapulted into a Paradox Realms, or hounded by Paradox spirits."

[url=http://whitewolf.wikia.com/wiki/Paradox_(MTAs]http://whitewolf.wikia.com/wiki/Paradox_(MTAs[/url])

In the tabletop RPG they're very different.

The idea behind true magic is that the mage is reshaping reality by the force of their will, so in the rules for Mage, there aren't really specific spells or anything, you just have influence over various spheres and can use them to produce effects. For example, if you have some expertise with the time sphere, you can speed up or slow down time and stuff like that, but the specific effects ("I want to freeze time around that enemy" or something) are up to the player casting the effect. There is no specific "stop time for one second" spell or anything, you just say what you want to do and the person running the game tells you how hard it will be and you roll the dice to see if you make it.

With thaumaturgy, like the other Vampire disciplines, the effects are specific and pre-set. There are a bunch of paths that give you more options if you learn them, but you're still very limited in that you can only do the specific things that the specific disciplines you've put points in to will let you. If you have A Taste For Blood, you can learn things from blood, but you can't decide that you want to use it to learn things from tears or potato soup or something, you are limited by what the spell will let you do and you can't change that.

Thaumaturgy works way better for video games, I think about 75% of the time I've put in to Mage has been arguing about casting magic with the players. But on the other hand, there's something cool about a rule set where the rules will let you do whatever you want.