Not quite. If you want the really nitty gritty, read my article on
The Fundamentals of Cache.
Here's the relationship between the Celeron2 and the P3 coppermine: Half of the cache on the P3 is disabled, which cuts associativity in half, and then they make the multiplier higher so that it won't support higher bus speeds quite so easily (read: they try to stick it at 66mhz bus).
When you say that its not a "scaled down" version, you're right. I was careful with my words. I said "scaled back". They are physically different cores. The Thunderbird just has more cache, but both are the same way associative.