Yes, these words do have a meaning in category theory. But for a haskell programmer, a functor is a type with a map operation, for a ocaml program it's a module

Yes, these words do have a meaning in category theory. But for a haskell programmer, a functor is a type with a map operation, for a ocaml program it's a module parameterised by a module signature. A monoid a type with a function T x T -> T. That's it. You can know these things and still know nothing about category theory.