This isn't much of a Linux question, but the only reason I'm wondering is because I want to know how much of a difference it makes for me to install slackpacks for the different architectures. I understand that i386 processors are a different architecture than i486, i586, i686, etc, correct? My question is this...what processors are what "architecture"? I have an Athlon XP (Palomino, I believe). Would that be i686? Thanks for the help!

yea. i386 processors are the i386 architecture. i486 processors are the i486 architecture...

pentium1 = i586
anything made by intel or amd after pentium1 = i686

i386 is the first 32-bit processor. anything below (like i286 for example) is 16-bit.

new instructions may be added without completely changing the architecture. for example: both the pentium3 and pentium4 are i686's yet the pentium4 has new instructions available to use by applications.

you can look at some x86 assembly books to get an in-depth explanation about the differences between the architectures.

just some comments :
you can use any architecture set below your, but none above, mean that you can use i386 package, but if some i786 packages appear from dark abyss of hell, you won't be able to use them (err... cuz their assembly code is too recent, not because they are coming from hell!!)