Depends on what era you're talking about. Metalcore was a term which has been around since the 1980s, although the bands it described are more often now referred to as 'crossover' bands. They were bands which played a blend of Metal and Hardcore Punk, but not to the point where they were considered Thrash bands, and there would typically be distinct segments of Hardcore Punk and distinct segments of Thrash or Speed Metal. Some examples include Carnivore, S.O.D., and Cro-Mags.
In its current form, Metalcore is supposed to be a similar principle, but, in reality, most of the bands currently described as Metalcore have little to nothing about them which is actually any form of Metal, and play a style which is exclusively a spinoff of Hardcore Punk (or derivatives of Hardcore Punk).

Ska-punk, Skacore, Neo-swing, hardcore punk, white rappers.

Skylime a punk rock hardcore band from buffalo NY

Son of Dork, Busted

Post-hardcore, melodic hardcore, straight-edge hardcore, emo (emotional hardcore), and screamo are all offshoots of hardcore punk.