This qualifies as one of the worst definitions of
Monad, but for the purposes of this article it will work fine.
Functor is more formally defined in terms of operations (
fmap) and laws (identity and composition).
Monad is more formally defined in terms of operations (
join) and laws (left identity, right identity, associativity).
If you’re after a complete formal definition, you’ll find plenty of articles online, so I won’t digress further here.