That's one of the many definitions we have for it, yes.

Plenty of people will disagree with it too.

Please correct me if I am off the right track here, but is not the distinction the fact that: in a "functional language" or maybe "parenthentical up-cup evaluating language"

functions are invoked in an encapsulating way, and no state is kept between function-cup-up-segments-of-code, but there is a R.E.P.L that (replies) when you invoke a (parens) which is, in LISP-land known as a program.

However, now that I have mind-dumped that ^ I recall haskell and erlang also being called "functional" but I don't know their syntax any more than a chimpanzee knows that the sun is round.

Functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions. A function is a rule that assigns, to every element of its domain, a unique element of its codomain.

Note that the above definition says nothing about how functions are to be evaluated: strictly, lazily, memoizing previously computed results, or using magic. No general-purpose programming paradigm can make such decisions for the programmer.