Three - Any difference between APNs?

3internet is intended for Broadband users and gives you a public IP address, whereas 3ireland.ie is the phone APN and gives you a private IP address behinds three's NAT.

If you don't need a public address (some sites my son uses don't work with 3ireland.ie) then use whatever works best. Sometimes one can be found to be faster than the other but there are no hard and fast rules.

Three don't give a toss what APN you use.