When a switch has the ability to learn what MAC addresses each of its
ports serves, then uses that to determine which port to send ethernet
packets out, what is that feature called?
That's called. Wait for it...switching. All switches do that, and it's a key differentiator between hubs and switches.
Also, does every switch with that feature also support ethernet
I need to spec out some switches that have this functionality but I'm
not sure what the correct terminology is.
If that's all you need, any $10 switch from your local tech store will do. Be advised, though, that you are going to want managed "smart" switches. You may not realize that want now, but you will kick yourself later if you purchase unmanaged switches.