Can liftM differ from liftA?

Question

According to the Typeclassopedia (among other sources), Applicative logically belongs between Monad and Pointed (and thus Functor

Answer 1

They can differ, but they shouldn't.

They can differ because they can have different implementations: one is defined in an instance Applicative while the other is defined in an instance Monad. But if they indeed differ, then I'd say the programmer who wrote those instances wrote misleading code.

You are right: the functions exist as they do for historical reasons. People have strong ideas about how things should have been.