"Functor" has been used in multiple ways in different fields. It's apparently a term of art in linguistics; we call C++ classes implementing `operator()` "functors"; Prolog terms have parts called "functors" (apparently imported from linguistics); and of course category theory has them.
As far as mathematics is generally concerned, I think the category theory concept is the origin. Monoids, on the other hand, did exist before category theory; the modern conception as one-object categories is nice, but it's definitely an import.
As far as mathematics is generally concerned, I think the category theory concept is the origin. Monoids, on the other hand, did exist before category theory; the modern conception as one-object categories is nice, but it's definitely an import.