Cobham's theorem establishes extensional equivalence, but extensional equivalence between classes does not entail that one characterization is machine-independent while the other is not.

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Classes(as mathematical/logical groupings): Groups or sets of objects that share something in common; a way of collecting similar things together.
Cobham's theorem(as referenced in computer science and computational theory): A mathematical result about what kinds of functions can be computed efficiently by computers; it connects the idea of 'polynomial time' (problems solvable reasonably fast) to a specific way of describing computations.
Entail(In logical reasoning and argumentation): To logically follow or guarantee as a necessary consequence; if something is true, what does it force to also be true?
Extensional equivalence(in logic and philosophy of language): When two different ways of describing something produce exactly the same results or refer to the same things, even if they look different on the surface.

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