[qntty]

Different how? They are both ways of making abstract descriptions of an object more concrete, which is analogous to the job of a programmer designing a data structure to concretely describe an abstractly specified computational object.

My point is just that in math, you can reason about an object even if you can't concretely represent it. For example, you can figure out properties of a number or function that you don't know enough about to write down. But in programming you can't use an object unless you have a concrete representation of it, and often getting that concrete representation (in both math and programming) requires a kind of work which is quite different than the work of abstractly describing or specifying it. So it's maybe not always appropriate to call an abstract description of a mathematical object a "data structure", since often it's more analogous to (say) the interface of an object than it's implementation.