P problems take polynomial amounts of time to solve(that's what stands for) Multiplication division etc.
Np problems take exponentially more time to solve as they get more complex(like sudoku) the problem is we don't know if they are fundamentally different types of problems. We don't know if NP type problems have fundamentally different ways of solving them then p problems. I and most of the community that knows about this think they are fundamentally different.
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Also it's primarily used for computers and whether they can solve a problem as quickly as they can check it. There are also two tiers (if I remember correctly) so you were close buuuutttt not good enough ://///////