Thrash also has some crossover with non hardcore punk, though I don't really know the difference between hardcore and normal punk. Anthrax and early Overkill fit that, and I think that the jersey/NY thrash scene might tend towards that.
Yeah, Thrash Metal has a LOT of hardcore punk influence. The cool thing about Anthrax was when they teamed up with Public Enemy and produced their electronic/hip hop/metal album...which in turn, unfortunately, created Nu Metal [Slipnot, Korn, early Linkin Park].
The difference between punk and hardcore is really in the sound. Punk and hardcore [real hardcore, like Bad Brains, Black Flag, Minor Threat, The Germs] have most of the same subjects but a really different sound. Typically, hardcore is faster, louder, and the songs [I find] are a bit more about the struggles of every day people, though I could be wrong, I don't listen to a lot of punk.
I think the best way to hear the difference between punk and hardcore is to listen to say.....Guns Of Brixton, by The Clash, and then Sailin' On, by Bad Brains. Or something from the Sex Pistols, and then Out Of Step, by Minor Threat.
They have different roots as well. Punk really does start with the British [The Damned, Sex Pistols, The Clash], though theres a lot to be said for MC5 and Iggy Pop and The Stooges having a huge influence on punk.
Hardcore really started in D.C., in the early to late 70's, and early 80's....Bad Brains, then Minor Threat....The ever changing sound of Black Flag.
Anyways, I've found the best way to tell the difference between punk and hardcore is to listen to as much of each. Similar subject, similar passion, MUCH different sound...
*goes back into lurkdom*