No, it was called a Senior Airman. Very few Sr.Amn went to NCO school and took the rank of buck sgt. before just going for staff, so the majority of E4s were Airman tier, not NCO tier. Sr. Amn and Buck paid the same, both being E4, with the only difference being NCO school and tier, plus some advantages (priority) if you wanted to separate rats and quarters and were single. Oh, and the star on your sleeve was silver instead of blue, although that isn't a perk, just an indication you were an NCO.
Note that most of the "exceptional" airmen back then would simply go below the zone (make E5/Staff Sgt. in less than 4 years) rather than seek buck sgt. Bucks were fairly rare for a variety of reasons, including the above.
Yes, I was in the Air Force. So was most of my family.