This gets confusing and as you go back in time there is little consistency from wing to wing and from deployment to deployment.
These days, every squadron on the boat has a "CAG bird", so the term "CAG bird" no longer suggests that the CAG will be flying an aircraft. Each squadron gets a plane with a fancy paint job. These days, you'll probably find one plane wearing the CAG's name.
If you go back a few decades, there was one CAG bird in the wing, although it wasn't uncommon that the skipper of a squadron also had a plane with fancy paint.
There are a few issues when it came to names. An F-14 squadron had room for 24 names in the pilot position and 24 names in the RIO position.
An S-3 squadron might have only four or five slots for pilot names. So on this rare occurrence, a CAG might defer to accommodate the squadron guys and his name might end up on his secondary aircraft in a fighter or attack squadron.
In this case, I'm betting that the CAG was based in the same location as VF-2 (probably Lemoore), qual'd and current in the F-14, and logging more F-14 time than S-3 time.