I think it's clearer to think of map as a function
(a -> b) -> (f a -> f b)
i.e. one which lifts function application over values of the functor. This is then analagous to the role of `f` for mapping types, and corresponds to the concept of a functor in the category of types. This relationship is harder to see in the tupled version. There's a similar argument for e.g.
