Noted on the terminology. I will be more specific-Isn't one of those slopey front tanks perked already? 
Yes, but that are entirely different vehicles. Different chassis, guns, everything.
The Jagdpanzer 38(t) "Hetzer" was based on the Pz 38(t) chassis (essentially a Czech pre war tank) with the 75mm gun we know from the Panzer IV lightly armored, but very tiny and heavily sloped
The perked Jagdpanzer IV/70 was pased on the Panzer IV, mated with the Panther's KwK.
The perked Jagdpanther was based on the Panther tank and carried ther same 88mm gun the King Tiger featured.
The only thing those three vehicles have in common is the basic concept.