Since the startx command starts the X11 client and server maintained more or less straight from the X.org project, and the sway command does not start any code that came from the Wayland project, I'd say that counts as "switching to Sway".

Wayland is the implementation detail in Sway to have a display protocol your Gtk, Qt and XWayland apps use to draw themselves, really no need to draw more attention to it than necessary. It's the Sway implementation that does all the magic.