The Weekly Standard‘s current issue has an article entitled “The Culture of Celebrity” on the current nature of fame and celebrity in the US. It tends to dwell more on the differences between fame (renowned for what you do) and celebrity (the seeking of recognition no matter whether you deserve it).
Fame, then, at least as I prefer to think of it, is based on true achievement; celebrity on the broadcasting of that achievement, or the inventing of something that, if not scrutinized too closely, might pass for achievement. Celebrity suggests ephemerality, while fame has a chance of lasting, a shot at reaching the happy shores of posterity.
The concept of celebrity, per se, is a relatively new one. More than 100 years ago, it was rare to find celebrities, i.e. those who are famous for being famous a la Paris Hilton. Instead, those who were famous had their renown for a reason, whether good or ill, some type of achievement. They were statesmen or religious figures or warriors or learned men. Whatever it was, they had done something to earn fame.
But with the rise of the various forms of mass media—newspapers, movies, radio, and television—we have also seen the invention of celebrity and it has not been a boon to our society.