Don't make the mistake of thinking that translating a type signature into written English gives a canonical description of the function. The first definition says "(a -> b) -> f a -> f b" - that is it.

You can translate one into the other easily

    map' :: (a -> b) -> f a -> f b
    map' i j = map'' j i

    map'' :: f a -> (a -> b) -> f b
    map'' m n = map' n m