I have had few celebrity and famous people experiences, sometimes through work and sometimes not.
The most famous person I have ever met was the Queen of England I had lunch with. She was a patron of the school I went to at the time. There was definitely no treating her the same way as everyone else though. We were given lessons in advance on how to address her, how to behave etc. And the security was so tight. It was like "don't put your hands in your pockets near her because security will shoot you" type of thing.
But the Queen isn't really a celebrity, she's a head of state, so it's understandable.
I have also met a number of ambassadors and other dignitaries. They are usually very polite, nice people. Or at least that is how they come across.
I don't really move in the upper circles of society as a norm, but my work sometimes takes me to these events as my old school networkr used to - I'm not particularly involved anymore, so it's far less now.
And then when it comes to celebrity, my most personal experiences were with one of my best friends who won a big singing competitions back in home country and enjoyed a year in the limelight before tragically dying in a car crash. Going out with him during that year was bizarre. To me he wasn't a celebrity, he was my friend, but going to a festival with him was absurd as hundreds of people wanted a piece of him. I found it very intrusive and almost scary and decided never to get famous. It's worked pretty well so far!