It's a built-in domain name unique to Pi-hole. It allows the Pi-hole to be reached via a fixed name regardless of the hosts setup or the interface in use.
The Pi-hole normal hostnames (and IPs) continue to work and identify specific hosts as expected (your second screenshot example).
Use whichever variants make the most sense at the point of operation.
I don't think you can in v5, not without hacking the code (someone will correct me if that's wrong), whereas in v6, which is in beta at the moment, you can.