Tanks and tank destroyers are not differentiated by whether they had the gun mounted in a turret or casemate. They were differentiated by role.
At the time of WWII, tanks were intended to be mobile anti-infantry weapons. They were capable of breaking through enemy defenses that didn't have anti-tank weapons and then exploit the breakthroughs with their cross country mobility. In defensive roles, they could crush infantry led attacks by being rushed to the scene of a breakthrough. Tank destroyers were vehicles designed to destroy tanks, but otherwise not support infantry. Two basic philosophies were held with tank destroyers. Heavily armored, low field of fire TDs were fielded by the Russians and Germans (Ferdinand, ISU-152, etc). These weapons often doubled as assault guns, designed to close on fixed fortifications and destroy them with frontal assaults. The Americans chose lightly armored, extremely fast turreted designs for TDs. The Wolverine and Slugger TDs, for example, were designed to race to, engage, and choke off any potential breakthroughs by enemy armor.
By 1942, though, the whole tank vs tank destroyer doctrine was falling apart. Tanks encountering each other on the battlefield became much more common as armor became a more integrated part of warfare instead of specialty units applied only at certain places in certain conditions. German tanks were inadequate against the Russian T-34s and KVs and the Germans rushed production of the Tiger I and spurred the design of the Panther and Tiger II designs. In turn, the appearance of these tanks spurred the introduction of the Soviet IS and T-34-85s.
Americans, experiencing some embarrassing tank combat in Africa and limited tank fighting in Italy held onto their doctrine until the very end of the war, with Shermans being 'tanks' and Wolverines, etc being 'tank destroyers.' American tanks were woefully undergunned until the very end of the war. American tank destroyers, being designed around a defensive philosophy that was rarely used in the attack of Europe usually functioned as light tanks. In few cases, such as Bastogne, was the American TD's high speed and mobility a real factor.
By the end of the war, heavy tanks, medium tanks and tank destroyers were being merged into the idea of the 'Main Battle Tank.' The Soviet T-54 was probably the first true example. This has been the predominant philosophy since the late 50s and continues today.