It gets even more fun, from the Wikipedia article on the Z80:
"The Z80 came about when Federico Faggin, after working on the 8080, left Intel at the end of 1974 to found Zilog with Ralph Ungermann, and by July 1976 they had the Z80 on the market.
It was designed to be binary compatible with the Intel 8080 so that most 8080 code, notably the CP/M operating system, would run unmodified on it. Masatoshi Shima, co-designer of the 4004 and the 8080, also contributed to the development of the Z80."
In addition, they still sell Z80 descendants, such as the eZ80, which is a binary compatible 24-bit version of the Z80, and variants of the eZ80 come with a 100mbps Ethernet interface on the SOC, along with 256kb of flash and 16kb of SRAM, and up to 16MB of external RAM without an MMU (more with one).
I think that turned out to be for the better as it made the mnemonics far more consistent and enabled the more complex addressing modes to be specified easily.
The only remaining inconsistency was "JP (HL)" (really should be "JP HL"), which Intel fixed with the 8086 when it adopted its variant of the Z80 syntax; the fact that both "JMP BX" and "JMP [BX]" are available on x86, and do different things, might've motivated this.
(Oddly enough, this inconsistency still exists in GNU/AT&T syntax.)
"Zilog wrote their own assembler and changed the mnemonics because Intel had copyrighted them."