I’m in the same boat. I flew in Saigon and out the same day. I don’t know why they came up with the term Vietnam “era” vet. WWII guys are all called WWII vets when out of all the ones I knew growing up as a child about 25% of them went overseas. But they were all WWII vets to me.
The American Legion considers me a "Korean era veteran" because I was in service in the US during the Korean war. The VFW considers me a "Vietnam Veteran" because I was in theater for nearly 18 months. I can't count my Korean era service for VFW membership because it wasn't foreign service. The distinction is a useful one.