Duet Mood Dissonance

Alice and Bob are taking part in a duet, whether it be an original song produced for the show or an already-"established" piece used for the scene. However, while they might be performing the same song - and thus, more likely than not, singing about the same subject - how they feel about it couldn't be any more wildly different.

Despite the name, this Duet Mood Dissonance can involve a trio, quartet, or more - the focal point is the difference in tone between two or more of the singers participating, which is usually accompanied by a change in instruments and key between their parts.

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

Examples of Duet Mood Dissonance include:

Film

"I Remember It Well", from Gigi, crosses this trope with Rashomon Style. It's obvious that Honoré has happier memories of that day than Mamita does (not that hers are unhappy).

Live-Action TV

Buffy the Vampire Slayer has this sometimes during the musical episode "Once More With Feeling". During "I've Got A Theory," Buffy ends the song by singing, "What can't we do if we're together?" She's singing about her resentment about them bringing her back from the dead, that she's stopped the apocalypse a few times and died twice. When the others join in, it's with genuine friendship and camaraderie that they can handle anything. It's also lampshaded in the finale song "Where Do We Go From Here," where Spike realizes he's joined in and says "Bugger off" because he doesn't care about the uncertainty of the future, his future has always been uncertain.
Psych: The Musical opens with this, fittingly for the song "Santa Barbara Skies". Shawn sings about how great it is that there's lot of murder for him to solve and be the hero, Gus sings about how Shawn is a fraud. They end singing about Santa Barbara, but with very different motives in mind.
During Scrubs‍'‍s musical episode, "Face The Future" has several characters sing about facing the future, but for different reasons. J.D. and Turk sing it to their patient Ms. Miller before giving her a CAT scan, while Elliott sings about telling J.D. she wants to live solo and Carla about her desire to return to work rather than take extended maternity leave.

Theatre

A case occurs in "I Know Him So Well" from Chess, where 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.
Fun Home has this often when present Allison and her father sing, "I can’t abide romantic notions/Of some vague long ago/I want to know what’s true/Dig deep into who/And what, and why, and when/Until now gives way to then". He's singing in her memory about vintage items he finds in neighbors' garages, she wants to figure out the truth of him being a closeted gay man that preyed on younger boys.
You're A Good Man, Charlie Brown: "Book Report" ends with the kids singing "A book report on Peter Rabbit". Most of the kids have finished...except for Charlie Brown who hasn't even started. Whoops!

Western Animation

In the Central Park song Can We Do Today Again?, Owen sings about how he messed up at being a father when he thought he would do well, while Paige sings about how she did even better than she thought as a mother. Where Owen wants the start the day over to have a second chance and do it right, Paige wants to relive the joy of being so awesome.
"Bob's Happy Place" from Bob's Burgers is a trio with only two of the characters on the same emotional page.
In the second part of "A Canterlot Wedding", the second season finale of My Little Pony: Friendship Is Magic, "This Day Aria" is sung by Chrysalis and Princess Cadance, and is about Chrysalis's evil plan to use Cadance's guise and ruinboth Shining Armor's happily ever after and Equestria's future. Of note is that Chrysalis and Cadence have the same voice actor.