Intel really struck it big when IBM's PC design used their 8088 as it's CPU.
The Intel 8088 was a budget version of the Intel 8086 - the money was saved by only giving the 8088 an 8-bit data bus instead of a 16- bit one.

So here's the thing...

IBM's replacement for the IBM PC - the IBM PC AT - used an Intel 80286.
A few years later, Compaq famously beat IBM to the punch when it came to shipping the first PCs with the next generation of processors - the Intel 80386.
And then we had the 80486, and then came the Pentium - a sudden name change which threw everyone, because they were expecting an 80586.
(US courts said you can't trademark a number, so Intel stopped using them.)

So we can easily see a fairly decent progression in Intel's numbering scheme. But isn't there a hole?

Shouldn't there be an Intel 80186?

Yes. And there was one. It just wasn't used in IBM PCs.

The Intel 80186 was an odd beast. It was designed to be binary compatible with the 8086, but at the same time it included a lot of features that were usually part of the supporting chipsets on a computer.
That made it more suitable for use in embedded computers rather than in IBM PCs, especially as some of those extra features actively clashed with the standards expected in an IBM compatible machine - so most computer manufacturers just skipped it and waited for the 80286.

A few plucky companies did use the 80186 in an "IBM Compatible", and one of them was where I first saw this chip. It was an RM Nimbus, a common machine in the education sector of the UK back in the late 80's.
And it was gloriously almost-compatible. It could do EGA graphics! Kind of. If you remembered to tell it to be IBM PC compatible, by running the "setmode" command first...

I still run across people who don’t believe that the 80186 existed. And before the internet, it was kind of difficult to prove that it did, unless you happened to have an example handy. So the debates could get a little circular...
Interestingly, although the 80186 isn’t remembered by the public, it evidently sold well. Intel stopped making the 80286 in the early 90’s, but manufactured their last 80186 in 2007 - less than a decade ago.

25 years is a pretty good run for a processor. Although perhaps not a good enough reason to waste neurons on knowing about it...