I read about the first computer I owned (Sord M5) and as far as I can tell it had the same CPU as ZX Spectrum. Is this correct?
Ah, the wonderful, classic Zilog z80! Yes, both computers had the same CPU, as did many other personal computers of the time, including the well-known TRS-80. CP/M had a z80 port, because of the architecture's popularity.
In fact, the z80 lives on today, and you've probably used one of them! Several Texas Instruments lines of graphing calculators use the z80. Every model (numerically) from the TI-81 up to the TI-86 uses a z80 processor, including the upcoming TI-84+ C Silver Edition (a color update to the 84+).