probably should have been posted in the music section.
i'd say skatepunk is overall more juvenile, less politically charged, lyrics tend to be more humorous, the music is often more melodic, broader mix of influences like ska, reggae or funk, without going really deep on them. there is serious skatepunk concerned about domestic violence or being a poor fuck up, but skatepunk is less socially conscious than old school punk and also less competent about addressing these issues imo. sometimes skatepunk is pretty much only comedic, like nofx. early skatepunk bands sometimes had a crew/locals only/kooks out vibe not unlike later nyhc bands.
it's hard to pinpoint it down to a certain sound or lyrical content. when i hear so and so is a skatepunk band i have this image in my head of dudes looking like random california/orange county skaters/surfers playing mediocre no use for a name style melodic hardcore, some others might think of suicidal or jfa instead because they are ten years older than me.
it probably has a lot to do with location and if the band bases their image on being skaters or being connected to skateculture.
myself i was never the biggest fan of skate punk or skate rock. i think a lot of it is just a shittier version of other styles of punk, hardcore or rock that i like. i also feel like a dork listening to music about skating. i already probably nerd out about skating too much, there's no need for me to have music also revolve around it especially when most of it is pretty amateurish in a bad way. if i'm at a bowl and someone starts to play broken bottles by grindline the band i'm not mad about it, in fact that track is pretty sick, but i can only get down with that stuff in moderation.
actually would rather listen to a band like turnstile, which i guess is somewhat a good representation of 2010s/20s skatepunk, than any of the 90s manchild bands singing about poop and stds or most the almost toxic and right wing 80s kooks out/skate cholo bands.