The Ubuntu 64-bit version is only for AMD processors?

Solution 1:

This is very confusing naming, but AMD64 (used to be called X86-64) as an instruction set standard is also being implemented by Intel 64-bit processors (except for the Itanium line of server CPUs, those use IA64).

So, yes, you can run it on Intel, too.

Check out the Wikipedia page for more details (including a list of supported processors)

Solution 2:

AMD64 and x86_64 should be the same.

The other 64 bit architecture is ia64, as far as I know.