Well, sort of. The Pentium 4 (as well as its Celeron) is essentially the same core as far back as the PII, with a faster core frequency, shrunken die size, new form factor, additional instruction set, etc. if you want to look at it that way. Furthermore, not all Pentium 4s have Hyperthreading enabled. The Celeron runs on a slower bus than the P4 B or C stepping, but equivalent to that of the first-generation P4s. The main downfall is that it can contain only 1/4-1/2 of the level 2 cache size of the P4, which can downsize on performance (e.g. a Celeron 2.0 GHz performing only equivalent to that of a P4 1.5 GHz)
In other words, the Pentium 4 is the much better deal if you can afford it. I could only recommend the Celeron if you use your machine for basic tasks (e.g. email/web-surfing/MS Word, etc.), as well as casual gaming, but even for those, the P4 is still the better buy.