x86 means the same thing as old "IBM Compatable PC", was.
8086 was the first IBM PC, 80286 are known as "286's", 80386 were the "386's", 80486 was the "486's".
The next step was the 80586, and these are the Pentium 1 proccessors. And are simple called "pentiums". Also instead of adding the 80 before the name, people just stick a "i" like i586.
80686, are often refered to as i686 for intel686 proccessors, and that's the more sudo-technical name for Pentium II, Pentium Pro and above proccessors.
Like the AMD 2400+ thouroughbread would be considured a i686 level proccessor. Early k5's maybe 586 or 686.
Sometimes you will hear people refer to i786 proccessors. (to differentiate between Pentium4/AMD k7 newer stuff vs older PentiumIII/AMD k6-5 stuff)
but it all gets VERY fuzzy after 586/686 stuff.
Now all these proccessors are kept backware compatable to the old 386 stuff. So they are refered to collectively as x86 proccessors. So that "x" can be replaced by 3,4,5,6, or 7 and you will still be right.
Most distros used compile their apps to be backward compatable with 486 or 386 proccessors, but most people don't use that stuff anymore since it's so old. Gentoo Linux people will compile for specific x86 proccessors like the AMD k7 or Intel Pentium 4 for specific extensions that maybe able to make their computer just that much more faster, but that's dubious at best.
Other archatectures are different and require people to write or compile their programs differently in order to run on that archatecture. Since windows doesn't use them you don't hear much about them in places like
www.anandtech.com.
Apples for instance use IBM power970 (called G5) and Motorla G4 proccessors. These are from the PowerPC archatecture.
So sometimes you will see flame wars between Mac fanboys vs Intel/AMD fanboys arguing between the different virtues of x86 vs PPC or x86 vs PowerPC.
Other archatectures are Sparcs, which have a whole host of different versions and terms for different stuff. These generally come from Sun Microsystems. They have a few different 32bit and 64bit versions, I beleive.
Then you have Alpha proccessors which used to be Super-duper powerhouses back in the day. They were running 400-500mhz 64-bit proccessors, back when Intel was running 100-200mhz 32bit proccessors. But they lost out when AMD and Intel took to the MHZ and later Ghz races. These were made by HP until a couple years ago.
(then you have queer ones like S/370 or AS/400 stuff (which are old-school IBM mainframe/database style stuff, or things like ARM, StrongARM, and Fireball proccessors that compete with PPC for the embedded marketplace. These "low-end" cpu's are actually much more common then x86 PC's because they are used in everything. Then you have whole hosts of long-dead or specific-use archatectures that I have no clue about.))
AMD has added 64bit extensions/improvements to x86 so now are called x86_64 or AMD64.
Intaniums are sometimes called ia86, and are incompatable with x86 and AMD64 proccessors, but they can run x86 programs in a special (and slower) compatablity mode.
Then you start getting into Mips vs Risc vs Cisc proccesors which are highly technical terms and don't mean nearly as much as they used to. Mips were old school stuff. A current example of a Mips proccessor is the Sony Playstation 2's cpu. I think that PPC was started off being Risc and x86 were Ciscs. But you can ignore this last bit of info if you want, the lines are much more blurry they they were just 5 years ago.