The numbers relate to the 'generation' of a processor, and the lower the number, the more computers it will run on. For example, something that is designated as i386 will run on anything from a 386 machine upwards.
386 = 386 and above
486 = 486 and above
586 = Pentium and above
686 = PII and above.
So, a PIII would definitely be an i686 system.