Pretty much everyone is a fan of music in general or some kind of music in particular. But I would counter that being able to name and differentiate a genre is a valid minimum standard to be a "real" fan of that genre.
I also reckon that being a fan connotes something different from merely enjoying the sound when you happen to come across it. But I guess there's room for disagreement there.
I highly disagree. I'm not going to say someone isn't a a true fan of Bach and Vivaldi because they refer to the music as "Classical" instead of "Baroque." Saying they "merely enjoying the sound when [they] happen to come across it" because they aren't interested in how other people have decided to name these things seems incredibly dismissive. Enjoying music is entirely unrelated to being interested in where other people have decided to artificially create divisions and the names they give to those divisions.
I have had a hard time articulating this too. I really like trains, I travel to go ride them, but I don't sit on the internet researching trains in my spare time and I don't know thr minutae of the different train models. I just know what I experience, and love it when I do.
When I tell this to normal people they think I'm a superfan, but I am not even in the same conversation as actual train fans. I doubt I could even hold a conversation about trains with a train fan.
It is the same for music, and I have the benefit of having been both a superfan and now later just a regular person who loves the music. I have an in depth love for the music, and no one can take that from my heart. But I don't give a lick about genres anymore.
I also reckon that being a fan connotes something different from merely enjoying the sound when you happen to come across it. But I guess there's room for disagreement there.