Perhaps you can explain why you think they are similar, to begin with. Show your understanding.

One's a fallacy and one's a kind of argument. Similarity doesn't much matter, as a) similarity is in the eye of the beholder, and b) similarity implies difference. It's the difference that makes a difference. Or, one's an argument for something; one's an argument by way of something. Enough?

I've never really got transcendental arguments. It may be my attention span. They tend to take so long that I just lose track and then at the end it says 'and therefore we have proven X by the transcendental argument', and I just go 'Did we? Oh, damn, I missed it again!'

Well, petitio principii is a fallacy in which an argument's premises assume the truth of the conclusion. It's a kind of circular argument. E.g., "Charles is a good person because he helps the needy, and anyone who helps the needy is a good person". In this case, the conclusion is assumed to be valid in the premise.
On the other hand, a transcendental argument is an argument in which it's negation implies in a contradiction because it's validity is a necessary condition for you to negate it. E.g. "I think, therefore I am". In this case, existing is a necessary condition for me to think, and I'm thinking, so I exist.
For me they seem to be similar, because in both there is a thing which is assumed to be valid and cannot be negated.
No.

For me they seem to be similar, — Nicholas Ferreira

As noted above, similarity isn't relevant. But you seem to have a grasp of them both; I have to suppose you can tell the difference between the two.

Or maybe you're thinking that begging-the-question is a special case of a transcendental argument. It isn't.

"Charles is a good person because he helps the needy, and anyone who helps the needy is a good person" — Nicholas Ferreira

Hmm, this isn't a petitio principii. The major premise may not be sound, but there's no logical fallacy being committed here:

P1: Anyone who helps the needy is a good person.
P2: Charles helps the needy.
C: Charles is a good person.

Perfectly valid. Maybe not so perfectly sound.

Ironically, your example of a transcendental argument ('I think therefore I am') would count as a PP, insofar as the premise does contain its conclusion - the 'I' (things are in fact more complicated with Descartes, and strictly speaking this is an enthymeme which means that it's missing a stated premise which would complete the syllogism and make this a proper TA but we can ignore all that for the sake of argument).

In any case, while you're right that both share a reliance upon certain assumptions, the kind of thing that is assumed in both are different. In a petitio principii, a conclusion is assumed in the premise. That's just the definition of the PP. A good transcendental argument however, 'assumes' a conditional: Iff X, then Y (or reversed: X iff Y). And I put 'assumes' in quotation marks because the soundness of this conditional itself ought to be something argued for, which means that a TA should, ideally, form one part of a larger argument rather than subsisting alone, unlike a straightforward syllogism. A 'bad' TA, which assumes its conditional without further argument, may indeed fall into PP territory.

The thorny parts of a TA deal with issues of necessity and sufficiency: is X both sufficient and necessary to guarantee Y (and thus fulfil the conditional, which would in turn complete the TA?); These are not really questions which arise with a PP. There's alot more that can be said, and the details of TAs can get real complicated real fast, but hopefully this goes some way to show why one can't straightforwardly identify TAs with PPs.