Bro tip: when trying to compare genres, listen to samples or important songs in the specific genres, and try to compare them. Mathcore isn't ALL about weird time signatures - they can be found in jazz, math rock, electronic music, most genres really. Mathcore is like a mix between math rock and metalcore. I don't know musch about the genre myself, but my tip is checking out the bands and albums listed in
this Wikipedia article. This forum has good educational threads about genres, they are totally worth checking out. I find them more thrustworthy than wikipedia articles. Links:
Punk
Emo
Screamo
Rock, metal and progressive rock
Progressive rock
Rap
Ska and reggae
Indie
Jazz and blues
Electronic
List of soul and funk artists