They are not equivalent, as Erlang/Elixir uses structural typing whereas Haskell/ML uses nominal typing.

In Erlang you can define the following:

  equal(X, X) -> true;
  equal(_, _) -> false.

In Haskell, the following does not compile:

  equal x x = True
  equal _ _ = False

instead, we need to write something like

  equal x y | x == y    = True
            | otherwise = False

A subtle difference, but in some cases the structural semantics really do make patterns a lot cleaner (shorter without sacrificing readability). I think that this style of pattern-matching semantics is a consequence of Erlang's roots in Prolog, which works similarly (and not only checks for structural equivalence but even does unification when necessary).