I think that a distinction can be made here. Consider the device as an XOR gate. There is no element within the device that is not a fundamental part of the XOR

I think that a distinction can be made here. Consider the device as an XOR gate. There is no element within the device that is not a fundamental part of the XOR system. The AND gate arises as a natural result of constructing the XOR gate. This feels fundamentally different from constructing an XOR gate, and then adding an AND gate. On a meta-level, in writing the above comment, I feel as if we are missing some critical vocabulary that would make this entire question seem trivial. Any ideas on what this vocab. is?