For me, fun vs critical listening is a hard split between work tasks and “play” tasks.
Fun listening is gaming, watching movies, or listening to music either for relaxation or as background audio when I write.
My regular day job that isn’t writing a bunch of crap on the internet involves editing a lot of audio files, so that’s my main “critical listening” task. I also listen very critically to a particular set of music files I’m intimately familiar with whenever I review a pair of headphones.
On rare occasions I also review an album, and I consider that a critical listening task.
These lines are usually how audio companies define those things, too.
I imagine most mainstream consumers aren’t going to be editing a lot of audio files or listening to music for the purpose of track analysis. And so they probably want fun headphones. Fun headphones are designed around minimizing treble fatigue, and usually have slightly enhanced bass to give them a more enjoyable, in-your-face quality.
Critical headphones tend to have harsher treble that’s good for picking out flaws in audio, or hearing hiss when you’re doing things like recording or mastering audio.