x86 and x86-64 (x64) are not mutually exclusive. x86-64 is a superset of x86, with 64-bit instructions. Many people still run 32-bit (x86) applications and operating systems on 64-bit processors. The reverse is not possible, though; you can't run a 64-bit system on a processor that only supports 32-bit.

x86, x86-64, and PowerPC.

The X86 64 is considered to refer to the central processing unit for computers. The X86 64 predominantly supports both physical and virtual memory on computer systems.

Actually, they both make what are known as x86-64 processors, which are processors that can run both 32-bit and 64-bit programs. Check the specifications of the processor for something like "64-bit" or "64-bit Ready" to make sure you can run both x86 (32-bit) or x64 (64-bit) programs!