Descriptive complexity results like Fagin's theorem presuppose fixed finite ordered structures, but the P vs NP problem ranges over all computational models regardless of representational assumptions.

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Computational models(as used in computer science): Theoretical frameworks that describe how computers process information and solve problems, used to understand what's possible to calculate.
Fagin's theorem(named after the logician Ronald Fagin): A mathematical logic result proven by Ronald Fagin showing that a certain type of logical language can express exactly the problems that computers can solve efficiently (a class called NP).
Finite ordered structures(as used in mathematical logic): Mathematical objects with a limited number of elements arranged in a specific sequence or hierarchy; think of a small list of numbers arranged from smallest to largest.
P vs NP problem(as used in computational complexity theory): One of the biggest unsolved questions in computer science asking whether problems that are hard to solve are also hard to check if an answer is correct; most computer scientists suspect they're different, but no one has proven it.

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