The common definition of security (for some cryptographic primitive) is to be secure against any PPT adversary (any probabilistic algorithm which runs in polynomial time). At the same time, we assume that underlying problem in this primitive is NP problem (the set of decision problems solvable in polynomial time by a theoretical non-deterministic Turing machine, link).
Is PPT algorithms are the same as non-deterministic polynomial? If yes then I am probably missing something, but for me it looks like any NP problem is solvable by some PPT algorithm (by definition of NP class), and so - what is the point of defining security against PPT? I understand this statement is false, but can't find out what exactly I am mising.