The cores themselves are both forged on the same 0.18 micron process, and it has been said that the Celeron II core is in fact a Pentium III E core with half the cache disabled.

This has been hinted at by Intel, and it would make a great deal of sense. Instead of requiring a new production line, they can just take chips from the existing Coppermine process, and modify them so that half the cache doesn´t work. This may seem like a waste of money, but it is far more efficient for Intel to be able to churn out one chip and modify it later, than it is for them to have two separate production lines.