The everyday meanings of these words are misleading when applied to the context of a particular programming language. Variables in one language are not at all related to variables in another. Mathematical variables, for example, do not change at all. Similar differences exist for functions and objects. These highly-overloaded terms are a constant source of confusion for people trying to learn different programming languages.

Monoid, on the other hand, has no such problem. If you look it up, its meaning in mathematics directly translates to its meaning in Haskell.