Pentium III 1GHz is only an 866Mhz model
Intel's Pentium III with 1GHz, which was widely announced some time ago, was purely a PR campaign. As it turned out, the clock was only achieved by overclocking an 866MHz model.
It looks like Intel's PIII on 1GHz was a pure PR action. You can only get to 1GHz by using an alpha cooler and increasing the FSB. That would also explain why the 1GHz PIII was priced at over US $ 300 cheaper than the 1GHz Athlon and why this corresponds to the price of the 866MHz CPU. The benchmarks of the PIII-1GHz that can be found on the Internet should also come from an overclocked PIII-866MHz.