The word "genre" comes from the French usage which meant "type, kind or sort". Basically it's a generalization of the style of music. The short answer to your post would be - yes, genres do have a correlation to playing style. Most of which are pretty obvious when you listen to them. Like you pointed out tunings and tones generally CAN distinguish a genre but they don't always place the music into a specific genre. For instance, you can have a band that plays all their songs in open tunings with slide and you would think that'd be country or blues... but depending on how they structure their songs, it may be rock or even metal...
Further, the things that are confusing you are what's called sub-genres. Their are countless sub-genres that have been created by artists to explain their music more exactly than a generalized genre... Some people might call their music Indie Pop, Indie Rock, Deathcore Metal, etc... Mostly this is an attempt by a band to sound different than someone else or to attract a certain type of crowd. In my experience, if a band doesn't know what the hell to classify their music as... or if they don't want to simply be called "rock" they just add the word "Indie". Also, ssame goes for metal... there are countless sub-genres of metal. Most of which all sound the same to me as well. But I'm not a metal head...
In conclusion, genrefication of music is somewhat out of hand at this point. Bands are constantly trying to find ways to seperate themselves from other people and trying to be different than their peers.... This has bred all these sub-genres that get thrown around.
