Was the basic idea that without a turret the chassis could carry a heavier gun with a longer range?
During WWII two very different types of vehicles got called "tank destroyers". The first was the US whos analysis of the Battle of France was that towed artillery was too dispersed and too slow to meet the fast flowing modern battlefield in enough numbers. So they concieved of a form of mobile anti tank guns that could be held in reserve then employed en mass against a potential break through of massed armour. Because of the sheer weight of allied armour, this was rarely needed (they did operate as designed at the Battle of the Bulge).
The Germans began with the idea of an "assault gun", a mobile artillery piece that could travel with fast moving infantry to attack strong emplacements. They started building them on Panzer III hulls as they were cheap and the lack of turret was for cost savings. Fast forward into the Eastern Front and they urgently needed a much bigger gun, but the Panzer III could not handle it so they re-purposed the idea of the turret-less assault gun to an anti tank gun. There was a lot more space in the hull than the turret for the recoil of the big new gun, it was cheaper than a tank and the low profile made it hard to spot\hit. As the war wore on, factories producing older tank types where changed to various type of assault guns to get big guns on mobile platforms, though they also built all manner of monstrous assault guns on everything up to a Tiger II hull.
The Germans almost always gave their assault guns to artillery branch and they were integrated into infantry divisions (or close to that). The US set up an entire Tank Destroyer branch, separate from the armour and artillery. Though the US ended up mostly using their TDs as assault guns while the Germans mostly used their assault guns as tank destroyers. The British just gave their US TDs to artillery branch to operate as mobile anti tank guns. They did develop a couple of vehicles in the mould of the German assault guns, strapping the brute 17 pounder onto dated Valentine hulls.
Valentine with the 17 pounder. They also gutted the inside of Sherman turrets to squeeze (just about) the 17 pounder into that turret as the Firefly. The barrel length allowed a very large powder charge to be used and gave the gun one hell of a velocity. The down side is up would set fire to the cover it was behind and blind the crews at night.
Firefly, (not a tank destroyer)
Very early Stug iii, really just an infantry support gun platform.
US M36 with a 90mm gun
And the Soviets just had to go that little bit bigger.
ISU 152 with a 152mm main gun. Had a really low rate of fire so I think it would have been mostly an assault gun, really not going to be much good at spotting falling shot on a moving target with 3 rounds a minute.