What is a word for the sensation when during a conversation you realize you were both talking about different things?
be at cross-purposes
at cross-purposes:
If two or more people are at cross purposes, they do not understand each other because they are talking about different subjects without realizing this: I think we've been talking at cross purposes - I meant next year, not this year.
Catch the wrong pig by the ear
the porcine reference is unlikely to be flattering but might not land you in any trouble if the person is crazy and at cross-purposes the whole time.
Talking past each other might work.