The GB/GBC does not have a real Z80, it has a different processor similar to the Z80. It lacks some instructions that the Z80 has, and also has a few instructions that the Z80 does not have.
Also, there is no version number on the GBZ80. A GBC game can tell if it's running on a GBA based on the bootup content of the B register (B=0 on gameboy, B=1 on gba).
The GBZ80 is just the CPU, the ppu is drawing all those 2-bit backgrounds and sprites. The sound chip is doing all the sound.
The GBZ80 is inaccessable to any GBA games, but the GB sound chip is still accessable. The old gb sound channels even have new features which not too many gba games have used.
It's still unclear whether the DS will support running the old gameboy games or not though. Even if the DS doesn't support running GBC games, it's still possible to emulate some of the classic monochrome gameboy games in
Goomba running on a gba flash cartridge.