“Functional” means “functions are first-class citizens in the language” and typically mean a lot of core language features designed around easily creasing android manipulating functions as ordinary objects (so C#, C++, and Python don’t really count, even with more recent bells-and-whistles). Typically there is a strong emphasis on recursive definitions. But trying to pretend “functional programming languages” are anything particularly specific is just a recipe for dumb arguments. And of course, outside of the entry point itself, it is quite possible (even desirable) to write side-effect-free idiomatic ISO C.
The “original” functional language was LISP, which is impure as C and not even statically-typed - and for a long time certain Lisp/Scheme folks would gatekeep about how a language wasn’t a Real Functional Language if it wasn’t homoiconic and didn’t have fancy macros. (And what’s with those weird ivory tower Miranda programmers?) In fact, I think the “gate has swung,” so to speak, to the point that people downplay the certain advantages of Lisps over ML/Haskells/etc.