Both languages are Turing-complete, so there's nothing that can be done in one and not in the other. The difference between the two is in the syntax.
Elixir developers use Erlang libraries because there are some excellent Erlang libraries out there and one of the advantages of living on the BEAM (Erlang VM) is that interoperability. (Just like how JVM languages get access to the vast array of Java libraries.) The most prominent example is Phoenix (popular Elixir web framework) using Cowboy (popular Erlang web server).
As Elixir continues to grow, you'll see more of the reverse, too: Erlang developers grabbing a useful Elixir library to use.
You can see packages for both languages (and they're all useable by both languages) at https://hex.pm