Higher order functions, what does the data do for you? (Thinking out loud)

A while ago, i thought about how higher order functions in a language require garbage collection.(All be it without loops, afaics.)

Now, i understand how to use recursion pretty well. Recursion provides one with a stack, so the implementor does not have to keep track of that data himself.

So, this brings up the question, can i understand the data higher order functions keep for you the same way i under stack, and does this suggest other ways of coding that are better?

Maybe i haven't read enough books though :), maybe it is obvious to some people.