Name of the difference between an asymptote and the curve that approaches it

Question

Consider a function, say a hyperbola, and its asymptote.

Is there a specific term for the difference between the two?

Answers specific to hyperbola, as well as answers about general terminology, are both useful.

A quick read on Wikipedia on asymptote and hyperbola did not turn out an answer and I don't recall having encountered any relevant terminology in my studies.

Answer 1

I have never encountered such a term and nobody else seems to know a relevant phrase, so it is likely that no such word exists.

Nonexistence is difficult to prove, so this is likely as good an answer as there is.