Similarities:

TRP: Woman spin the hamster wheel to come up with rationalizations for their behavior.
PUA: Women act on their emotions in the moment and only come up with rationalizations after the fact.

Differences:

TRP: It's possible to reliably tell if a woman has a promiscuous history or not.
PUA: It's not reliably possible to tell how promiscuous a woman has been, so assume they all are.

TRP: If a man stays alpha within his relationship, she won't cheat on him.
PUA: Entering into a monogamous relationship automatically decreases the woman's perception of the man's alpha status for at least the life of the relationship. Ditto for moving in together.

TRP: A promiscuous woman is unworthy of a long-term relationship.
PUA: A man shouldn't enter into a monogamous long-term relationship at all, so it doesn't really matter how much sex she's had.