P and NP are not the machine, but the set of problems solvable by deterministic/non-deterministic Turing machines limited to a polynomial number of steps. P^X is set of problems solvable by a deterministic Turing machine with access to oracle X, which is fairly straight forward, but need have little to with P. Similarly, NP^X is the set of problems solvable by a non-deterministic Turing machine with access to oracle X. However, this means if there's any input it could ask X to get an answer it can use to solve the problem, it can solve the problem, which may be vastly more efficient than trying to construct the right question to ask.
Essentially it boils down to: Just because two different models of computation can solve the same problems, does not mean that when augmented by the same oracle can solve the same problems (they can access the oracles in different ways).