"State actor" is a who. "APT" is more of a "how". It describes adversaries who are very technically sophisticated ("advanced"), and who can remain in your network undetected for a long time ("persistent"). Another aspect of "persistent" is that they can be very hard to eradicate - you have to find all the backdoors that they left on all the machines.

overlapping but non-equivalent terms; state actors are often APTs, but not all APTs are state actors (criminal gangs etc)