Yes. The external bus on the 8088 is 8-bit while the 8086 is 16-bit (which is why the 8086 wouldn't appear in a PC until the mostly-80286 PS/2 line, since the 8086 and the 80286 could use the same 16-bit PS/2 bus).
There were numerous 8086 PC compatibles before the PS/2 or the 80286 became popular. The most famous was of course the original Compaq Deskpro, but At&t, Wang, Eagle and others did too. Yeah, the BIOS had to be aware of the difference between the 8088 and 8086 for some setup stuff, but the 8086 is at the hardware level perfectly happy to talk to an 8-bit bus and the software mostly never knew the difference.
edit: And how could I forget (as mentioned by another poster in the thread) the numerous NEC PC98 machines with an 8086 which created their own industry. Sorry for slight, Japan.
and what does that have to do with BIOS? The only way you can tell 88 from 86 apart in software is speed and executing self modifying code to measure processor 4 vs 6 byte prefetch queue depth buffer size difference.
With the exception of bus speeds / timings and the differently sized prefetch queue, the 8088 and 8086 are 100% software-compatible so there wouldn't need to be any difference in the BIOS.
Yes, I'm aware of the hardware differences, but were they significant enough to require software adjustments? I used both 8088 and 8086-based PCs in the second half of the eighties, and from a software perspective, they seemed identical. I assumed the same applied to BIOS code since, to the best of my recollection, software couldn't detect whether it was running on an 8088 or an 8086, even if it tried.
By the way, while the PS/2 series marked IBM's first use of the 8086 in a PC (specifically the PS/2 Model 25), clones had been using the 8086 for some time already. The 8086 worked seamlessly with the standard ISA bus, and as far as I know, no 8086-based systems used the PS/2-specific Microchannel bus.