Duet Mood Dissonance

One singer has one emotion, another singer has a wildly different emotion. They are probably apart and singing about their own situation.

Compare Lyrical Dissonance, in which the lyrics themselves contrast with other aspects of the song.

Theatre

 * A borderline case is to be found in "I Know Him So Well" from Chess, in which Florence and Anatoly's wife both sing about how well they understand his needs and motivations... and may as well be describing two entirely different men.

Western Animation

 * In the Central Park song Can We Do Today Again?, Owen sings about how he messed up being a father when he thought he would do a good job, while Paige sings about how she thought she earlier thought she doing a bad job being a mother and it turned out she was doing a good job. Owen wants this day to happen to start again so he would have a second chance and do it right that time; Paige wants the day to happen again so she can relive the joy of being so awesome.
 * This Bob’s Burgers song is technically a trio, but two of the characters are on the same page, so close enough.
 * In This Day Aria from My Little Pony: Friendship Is Magic Chrysalis sings about how her evil plan is going as planned while Princess Cadance, a victim of Chrysalis’s evil plan, sings about how Chrysalis’s plan is proceeding well. Obviously they have different dispositions on if they want the plan to succeed.
 * Fun fact: Chrysalis and Cadence have the same voice actor.