We use the name Coppermine to distinguish it from the two versions of the Pentium 3....one is the Katmai, the other is the Coppermine. The Katmai is the older one, with external 1/2 speed 512KB cache chips on the cartridge. Its transistor size is .25 micron.
The Coppermine has 256KB of cache integrated onto the core itself running at full speed, and has a much wider bus between the core and the L2 cache, creating faster transfer rates. The Coppermine has a transistor size of .18 micron, and has various other tweaks to improve performance over the older Katmai Pentium 3.