AMD64 is 99% the same with the Intel-64 Architecture. It's called AMD64
because AMD was faster than Intel in delivering. (And to Avoid confusion with
IA-64 (Itanium)).
You can use a 32 and a 64 Bit Operating System on them (but you are limited
to 4GB of Adressable Memory in 32 Bit Systems)
You can run a 32Bit Application on a 64 Bit OS, but you can't run a 64 Bit
Application on a 32Bit Operating System.
Processors supporting 64 Bit:
Intel: Some Pentium 4, all since Core2Duo and Core2Duo based Celerons, some
Atoms
AMD: All Processors since AMD64
64Bit Architecture has the Advantage of using more than 4GB of Memory and
some improvements on the executing of Code.
As disadvantage the System is a bit slower (while running 64 Bit OS because
you need more Ressources to manage Memory).