Haskell coding-style: map, fmap or <$>?

Is there any reason to prefer one of the following notations over the others or is this simply a matter of preference?

map toLower "FOO"

fmap toLower "FOO"

toLower <$> "FOO"

As an aside: I realize that <$> is the same as `fmap`. Am I right in the assumption that map is just a less general form of fmap?