The original version, Katmai was pretty much the same as the Pentium II, the only differences being the introduction of SSE, and an improved L1 cache controller (which was the cause of the minor performance improvements over the latter PIIs).
The second version, Coppermine, had an integrated 256k L2 cache, which greatly improved performance over Katmai. It was built on a 0.18 micron process. It topped out at 1GHz. A 1.13GHz version was produced, but recalled after it proved to be so unstable that it was unusable. Ironically, the problem was traced to the integrated cache, which simply could not operate at speeds above 1GHz.
The third version, Tualatin, was really just a trial for Intel's new 0.13 micron process. Had the Pentium 4 been on a sounder footing, it's doubtful whether Tualatin would have ever been made. Tualatin performed quite well, especially in variations which had 512k L2 cache (called the Pentium III-S). Intel didn't want a repeat of the situation it had with Celeron and Pentium II, so Tualatin never ran faster than 1.4GHz (Pentium M proved that the design was good for at least 1.7GHz on the 0.13 micron process).
The Pentium III was eventually superseded by the Pentium 4.
see also: List of Intel microprocessors