I'm going to have to go out on a limb here and agree that Broadway personalities are NOT celebrities.
Save for name dropping, last weekend I saw a production out of town with two rather large Broadway names. I happen to know one of them and went out afterwards with her and a few members of the cast. Firstly, it amazed me that there were so many people fawning over her at the stage door (since we weren't in Manhattan), but they were mostly college theatre students, so it made sense they knew who she was.
The minute we left the alley, not one eye turned to look at her that hadn't been in that theatre. At the restaurant there wasn't a trace of recognition. She was able to enjoy herself without fear that some random person was going to interrupt her meal hounding her with compliments and begging to take a picture.
Do you think SJP can sit down anywhere to eat without at least ONE person in the restaurant noticably POINTING at her the entire time?
That right there is the major difference. These personalities may be important to us because we value theatre and their talents, but it's almost like a tightly knit neighborhood. No one knows whats going on inside of our picket fences except us.
That said, there are obviously different levels of celebrity. Granted in todays society more people are going to know who Britney Spears is over Haley Mills (who I actually DID run into on the street when I was living in the UWS-- actually walked RIGHT into her). Of course, that doesn't make Haley any less of a celebrity. Most people do know who she is.
As far as the T.V. argument goes, try telling me the majority of people who DON'T watch T.V. can even COMPARE to the majority of people in the world who have no interest in theatre and can't honestly name one musical sans CATS, POTO, HAIRSPRAY, RENT, or WICKED?
"You! You are the worst thing to happen to musical theatre since Andrew Lloyd Webber! And you, well, I just plain don't like you."
~Stewart Gilligan Griffin