When to use "retake, make-up" for an exam?

Hello,

Is it acceptable to say that if you are unable to take an exam, then you may retake it?

A friend of mine insisted that this is wrong and the only term I can use in place of "retake" is "make-up." I argued that it is acceptable to retake something if you missed taking it prieviously.

Are we both saying the same thing, different things, or is this a problem with semantics, logic or something else? Please tell us where we've gone wrong.

Thanks!