[Haskell-beginners] functor declaration

[Michael Mossey]

in the declaration of Functor:

class Functor f where
     fmap :: (a -> b) -> f a -> f b

does the compiler infer that f is a type constructor (not a type) because 
of the appearance of "f a" and "f b"?

What I'm thinking is that some classes are classes of types, not type 
constructors. Like

class CanMakeInt a where
    makeInt :: a -> Int

In this case a is a type, not a type constructor. But there is no 
difference in the form of the first line of the class declaration.

Thanks,
Mike