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.
Google search first result:
> monoidhttps://en.wikipedia.org/wiki/Monoid_(category_theory)