>>>Two different things.
>>
>>IMO, "two different" is redundant, because "different" is a relation between more than one. Or else you want to reclassify this back into normal jokes:
>>
>>Q: what is the difference between a parrot?
>>
>>A1: it has two legs, specially the left one.
>>
>>A2: the left leg is lefter than the right.
>
>OK then, how about "two of the same thing"?

Same as what? :)

I'm not exactly saying that "two different" is wrong, it's just redundant, specially in the "both different". It sounds as if you are emphasizing that not zero, not one, but two of them are different. Yeah - like the case when only one is different and the other isn't would make any sense.

Likewise, "two identical" or "two same" is also redundant, for the same reason.

It does make sense to state that two are same or different - after we have, say, examined them, when it's news to someone.