396th was actually a Heavy Bombardment Group in WW2 for a very brief time. It was activated January 29, 1943 and Inactivated May 1, 1944.
It was equipped with B17s and was at first an Operational Training Unit and then a Replacement Training Unit.
Track down a copy of "Air Force Combat Units of World War II", edited by Maurer Maurer.
It gives brief histories of all the units of the USAAF in WW2. I found it at Half Priced Books a long time ago and I've used it a ton for these kinds of questions.
398th Squadron was also a bomber squadron, part of the 504th Bomb Group flying B29s.
Looks like someone was using a bit of artistic license to come up with that combination of Squadron and Group for Fighters

Dan/Slack