I remember using IBM Key Punch Machines to do COBAL, RPG-II programs for an old Burroughs B1740 computer in my Senior Accounting & Computing class in 1981. BASIC was just starting out and the Z8080 processor was the newest thing. Wow, how far we’ve come!
the Z8080 processor
I think you're a bit confused. Intel made the 8080. The designer left, founded Zilog, and made the Z80. AFAIK, there was never a Z8080.
Followons to the Z80 included the Z180, Z280, Z380, eZ80, Z800 (which, IIRC, Hitachi knocked off as the 64180 and eventually got licensed back by Zilog as the Z180), the Z8000, and (don't know if it ever shipped) the Z80,000. Zilog also does a Z8 microcontroller.