The difference depends on when the person went solo. Sting was in The Police first, then went solo. He was never in a band after that, or created a band. Rod Stewart was in Faces first, then solo. Phil Collins was in Genesis, then solo. So obviously the bands they were in are not sub-categories! Paul was in the Beatles, then in 1970 he went solo. Then in 1971 he created Wings. After that ended he didn't have a band name and just had basically sidemen and he toured as just Paul McCartney. That's why his solo career is different. For many 1st generation fans, anything Paul did after the Beatles was "solo" even if he did name the group. I went to see Paul McCartney, not the other guys. It's jmho.
...and your jmho is a very valid one. But personally I think Paul being in group A,then going solo,then being in group B doesn't mean that group B is any less of a group than group A. Its just another group. But I think,as you infer, when you first become interested in Paul does alter the way you perceive what follows. In 1976 when I first saw Wings live,I went to see Wings and not just Paul. It was just as amazing for me to see Linda,Denny,Jimmy and Joe as it was to see Paul, as I'm sure it would have been for Beatles fans to have seen John,George and Ringo a decade earlier.