I guess the simplest way to think about it is that if stuff like Jungle & DnB are Punk Rock, then Breakcore is Hardcore Punk Rock. So yeah, more abrasive, more extreme, more chaotic & experimental, faster tempos, etc.
Breakbeat is a fairly context dependent term when it's being used to describe musical genres tbh. It can be used as an umbrella term for any type of music that uses sampled drum breaks. I.e. Hip-Hop, Jungle, DnB, Breakcore, Big Beat, etc. are all Breakbeat genres. However, it can also be used to describe a specific sub-section of breakbeat music, usually stuff that's more on the downtempo & midtempo side of the spectrum that doesn't neatly fit into other genres.
Not that familiar artists who make generic Breakbeat, but I think The Chemical Brothers and The Prodigy were/are both big artists for that type of music. You could also check out The Glitch Mob's latest album Ctrl Alt Reality, which is somewhere in between generic Breakbeat and Breakbeat Hardcore.
For Breakcore artists to check out, Venetian Snares is probably the best one to start with. Pretty big discography and also more on the IDM side of the spectrum.
Igorrr is another good one, especially if you're into Rock/Metal type stuff since their music heavily fuses Metal and Breakcore. There's also Alec Empire's album "The Destroyer," which is what I've usually seen credited as being the first Breakcore album (though from what I've heard, Alec has become a bit of a right-wing shithead in recent years, so probably try not to give him any money if you're gonna listen to it).