Celerons are cut down versions of Pentiums. So there is a Celeron that's a cut down version of a P4, another that's a cut down version of a P3, and in the past there was one that was a cut down version of a P2.
What is cut down is the local cache memory, sometimes the FSB speed, and they're always a few steps behind the fastest Pentium speed. however they vary somewhat, dependant on which models are being considered.
As budget processors they are excellent, stable and cool running and very inexpensive.