As far as I can remember, the Altair used an Intel 8080A processor. The Intel 8008 wasn't widely used by hobbyists. I don't recall any CPU with 8800 designation from that era. Possibly RCA or TI, but neither were used by Altair.
The Motorola 6800 and Mostek 6502 soon became more popular because they were easier to interface than the Intel 8080A. The Zilog Z80 came out a couple of years later.