I'm old enough to remember when "alternative" was called "new wave". It's been a question of what it is an alternative to.
To me, "alternative rock" is anything that's NOT like Journey or Foreigner. Even Soundgarden (which was little more than updated Sabbath and Nazareth) qualified as the A-word.
"Punk" is even more diverse. The Sex Pistols are considered punk, but they don't sound anything like bands like the Dead Kennedys or Black Flag. The Clash, Ramones, NOFX, Bad Religion, Circles Jerks, UK Subs, Minor Threat, Fugazi, Husker Du, Blink-182, Green Day, Offspring and on and on all loosely fall under the "punk" umbrella without being that much alike to each other.
And when you factor in hyphenated genres (rap-metal, trip-hop) you could go crazy sorting the record collection any other way than alphabetically.🙂
Don't worry about what category music belongs to and just listen to it! To me, there are only two kinds of music - Good music and that crap you're listening to!😉