Interesting so AND and OR do opposite things when the inputs are different. But when the inputs are the same, they both do the same thing, that is the behave like an identity gate. So an AND and OR gate both preserve the inputs when they are equal, but one(AND) outputs false when the inputs are different, and OR outputs true when the inputs are different.
So an AND kind of behaves like an Identity gate and a zero gate. And an OR behaves like an identity gate and a one gate. With equal inputs it functions as an identity gate, and with unequal inputs they function as either a zero(AND) or one(OR) gate.