[fmap]

You're right, maybe is equivalent to the type of lists with at most one element. There are however monad instances which are genuinely different.

For example the state monad is defined as

  F(X) = S -> S*X

I.e., a value of type F(X) is a state transformer which takes a state argument of type S and produces the new state and a value of type X. In this case, bind is sequencing of state transformers.

Using the state monad you can write code that looks like it uses a global variable of type S, while being completely pure which makes testing and refactoring easier, and of course doesn't pollute the rest of the program.