Let me ask you this:
Your ultimate question: There is this band, Band X. I want to know how their music sounds.
If you asked someone what genre Band X is in, and they said, "rock," does that really help you? Does that tell you anything about how they sound? Generally, maybe. Specifically, not really.
If you asked someone how Band X sounded, and they say "Oh they sound a bit like Band Y, and a little like Band Z. They have an acoustic foundation with piano and even some electric guitar, with catchy melodies," then you have a lot more detail than just a genre.
My point: Genres are becoming pointless and really don't do any band justice because they all sound different anyway. So when inquiring about Fun, you shouldn't ask for a genre.
I think that's part of the reason why there's 27537626 subgenres these days. Saying fun is a rock band doesn't tell you much, but calling them an indie-power-pop-rock band (or whatever) helps to specify.