I know it is a silly question, but when I tried to order or download some linux distributions, they have the options for i386, i486, i586, alpha, IA64, M68K, etc..

Does i386 mean intel-80386? Why when I told the webmaster that my pc is intel piii 933, he told me to download the i386 version? Isn't it should be i586 or others?

I pulled this off another site. Apparently, i386 is considered the safest. While others may work with your system architecture, the i386 is guaranteed to work.

i386 - Optimized for 386 and above processors (386, 486, 586 (Pentium), beyond).

i486 - You rarely see these if ever. Optimized for 486 and above processors (486, 586(Pentium), beyond).

i586 - Optimized for 586/Pentium processors (586 (pentium), beyond).

i686 - Optimized for that beyond category (Pentium Pro???, Pentium II, Pentium III, Penmtium IV, K6-x, Atholon, Duron, Celeron (later only???), Thunderbirds, etc).

src - Source package. These are rebuilt into packages and can optimize for whatever platform you have. They take the longest to install.

References:
linuxiso.org
resellerratings.com

With Linux, 386 is the lowest common denominator. Below that lacks hardware, instructions, etc that Linux now requires. There are specialized Linux kernels that will work on older hardware, such as ELKS, but you can't do a whole lot with a 200k kernel.

If you're only going to use a PIII, go ahead and get the version optimised for it. But if you might install this on other machines, get the 386 - that's the safe way to go.

Thank you for both of you. Thank you.