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.