What are the differences between the frames? Generally dropouts and sizing? With jump being in the smaller category and taking slightly shorter forks? Or is the geometry totally different.
All a bit different in theory but can be used for each thing... I'd say a 'jump bike' would be a very small frame, single speed, only a back brake, and either rigid or short travel and firm forks. Can be light if you are a smooth, experienced rider but generally built strong. 4x isligjter, has a front brake, has gears, suspension and a bigger frame. And a 'hardcore hardtail' is just a beefed up 4x bike. Alll generalisations there.
Hardcore hardtail can be used for all day riding.
Jump bike is for jumping.
4x is like a jump bike but with higher gears.
jump bikes and 4x bikes are generally similar although some 4x bikes will be longer. short chainstays, shortish TT, low standover. normally 80-100mm travel although some jump bikes are rigid specific.
hardcore hardtails range from everything from 4x bikes to 200mm triple crowned forked things. not easy to define them really.