ARM is a family of processors, sort of like MIPS, x86 or PPC.
ARM7 and ARM9 are specific families of processors, like the Intel P6 or AMD K7.
ARM7TDMI is a specific ARM processor core (the one used by portalplayer), much like the Coppermine is a specific P6 processor core.
The PP chips are ARM7TDMI cores. The similarity between ARM processors means we can use the same tools to compile for both. However, there PP chips also include many other things that on a PC might be included on the chipset or motherboard.
Hope that helps.