I don't understand your question. The phoenix frame work compiles to beam, and then just runs on the erlang VM. Are you talking about its process architecture or something? Phoenix isn't something that sits alongside the ErlangVM, it's just code that runs inside it. Phoenix does not have any built in way of handling databases, but by default installs Ecto, which is a framework for handling database interaction.
You should really just go read those links. Phoenix is much more than your standard client server REST architecture at even a high level due to its inclusion of channels. If you're interested in the process mechanics of how HTTP requests are handled at a lower level you'll want to look into cowboy and ranch.