when i download a distro it sais so and so for one of these so what do they stad for?

x86 is the CPU architeture family. These go along the lines of i286, i386, i486, i586, etc. where the x is used as a variable for the 2, 3, 4, 5, etc.

i586 is the same as a pentium and amd k1, i686 is the same as pentium II and amd k2, and so on. x86-64 stands for 64-bit processors like Athlon-64's and Opteron that operate off of the x86 family.

Each of the chips has extra transitors and instruction sets, so if you download a distro that was compile for your chip, it should, in theory, run better. Also, You have to meet the architecture number or older to use the distro to.

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x86-86 is for 64-bit systems such as Opterons.

That is not true. The amount of transistors does not depend on architecture model. There are 686 or 80686 processors that have as much transistors as a 486 or 80486. Also adding more transistors does not always mean it will be better although it will be hotter.

I suggest doing a search in this forum on this topic. There are several threads for your question.

Extra Transistors, no. Extra Instructions, Yes. A linux distro compiled for i686 won't run as well on a i586 processor, but it should still run. If you see a distro for x86 it's a generic distro that will run the same on any series as long as it's the same processor speed. And, as mentioned above, x86-64 is for 64-bit processors and won't run on 32-bit processors.

Hmmm... For one, many of the chips DO HAVE more transistors, also, SOME programs will run on older arch's, however, some WILL NOT. In general, you should NOT use a distro that is newer then your chip family.

~everyone's gotta be so exact~

80386 has 275,000 transistors
80486 has over 1,000,000 transistors
80586 or Pentium has 3.1 million transistors
P55C Pentium has 4.5 million transistors
80686 or P2 has 7.5 million transistors

and I doubt the trend has ended but since this is the only ones Linux is compiled for that is all I will list
my research was done at Wikipedia
the more transistors equal more power more instructions and better processor's
true they may be hotter but it is well worth it

And I don't even have a 80586
the oldest chips I have are Pentium 3's
most of my stuff was donated I have 2 Xeon Quad cores
and 2 Pentium D Dual cores
and several Pentium 4's and a few Pentium 3's
I don't think I even own a 80586 any more
got rid of them a long time ago
to old and took up to much space

From a Linux kernel perspective, there are two main considerations:

1. 64-bit or 32-bit architecture: This is the most fundamental architectural concern. If you have a 64-bit CPU, as most people do today, you should always use a 64-bit OS build.
2. Processor model/features: Is this-or-that instruction available?

Most Linux "distros" are built for a fairly generic x86 or x86-64 chip for simplicity.