Okay, we can all agree that "classic rock" isn't a genre, since its contents range from The Beatles to Metallica, depending on the radio station.
However, we need to establish lines. When does rock become metal? When does alternative become grunge, and grunge become metal? What the fuck is alternative rock? All these topics will be addressed in the following tl;dr.
First, pop music. Pop music comes from the term "popular music", which, in theory, can encompass country, rock, metal and even jazz. Some have tried to force in such genres as "pop-punk", "pop rock" and "pop metal". Hell, iTunes "Genius" labels fucking Whitesnake as "pop metal".
Pop music immediately makes you think of Lady Gaga, Ke$ha and whatever else the world has thrust upon you. Most would say it's a full-fledged genre, and this isn't entirely without merit. Backstreet Boys and *NSYNC may not be popular any more, but aside from the "boy band" label, what are they? The "boy band" thing was a movement, not a genre. Some say The Beatles were the first boy band. Which, looking at it, is true. They're boys. They played music together, making a band. However, using this, Radiohead and Slipknot can also be called boy bands. What's Rick Astley now? Dance music? That seems designation-y to me, too. Pop music can't really be thrust into another genre, and has thus become a genre of its own.
Now that we have a baseline, where does one go into rock music? The Beatles are oftentimes considered pop music, however, I say that if you have guitar parts which are more than just backing filler in the majority of their songs and noticeable (and even sometimes thrust to the forefront [don't fore and front mean the same thing]) drums, you are a rock band. The Beatles are thus a rock band, seeing as even their popiest songs (I Want to Hold Your Hand even) have these qualities. Fuck, even their acoustic songs have guitar parts you're supposed to notice.
Now that we have the jump from pop to rock, let's go onto sir metal. Off the top of my head, this is the most borderline song I can think of. It has heavy guitar and pretty much everything that makes a metal song. The line here is far more blurry. I will go ahead and say that THIS SONG is the fucking line. Less heavy than Stone Cold Crazy? You're hard rock. Heavier than Stone Cold Crazy? You're metal. Hard rock. Metal. Hard rock. Metal. Hard rock. Metal.
However, Grunge is tricky on both sides. Bands like Alice in Chains straddle the line between grunge and metal so well, that it's hard to find a line. I propse this as the line. Pearl Jam straddles the line between grunge and rock. I propose this as the line.
Alternative rock is the ultimate genre.
It's pretty true. I stick Radiohead, R.E.M., My Bloody Valentine, Sonic Youth and fucking Brand New here. In fact, all of my "NOT SURE"s are Alternative. However, bands like Foo Fighters and Weezer fit outside of alternative, so fuck off guys.
Indie is not a genre. It's the boilerplate term for bands on an indie label. It's a selling point for wannabe hipsters and rebellious teenagers. Every "indie" band either sounds like a classic rock revival thing or some band that everyone agrees is alternative rock. I think I made my point.
Punk rock is hard to define, but I classify it as powerchords powerchords powerchords. I stick Good Charlotte, The Clash, My Chemical Romance and Blink-182 here. Most "emo" music is punk, which is where we get the term "pop punk". "Pop punk" is "emo" is punk. It's all the fucking same. Genres evolve, and that's how punk has evolved.
FINALLY
No post-genres actually exist. As I said before, genres evolve. Grunge didn't die, it sold out. Post-rock is just ambient shit. Post-punk is the evolution of punk. Punk-fusion may be more accurate, but, once again, the -fusion genres are the genres evolving. The only post- genre that holds any weight is post-avant jazzcore.