There is no x32 or x64. There is x86, which is an instruction set, but it has nothing to do with being 32 or 64 bit. There are x86 and x86-64 too, but they are the same, with an extension over the other.
That is how even registers got named. In the 8-bit era, registers were named like AL and AH (BL, BH, CL, CH, etc) (meaning A low and A high). Then later, when we ascended to the 16-bit era, they became one and named to AX, BX, CX, etc. After we reached the 32-bit era, they got 32-bit wide and had to find new names to be able to address its native 32-bit view, so they became EAX, EBX, ECX and so on (E meaning extended AX, etc). In the 64-bit era, they got wider again and got the name of RAX, RBX, RCX (R just means register, cause they already used E as extended, so they needed to find something else not to be ambigious).