Tank destroyers, past and present (yes, countries still make and deploy tank destroyers) were lightly armored, some having no armor on the top or rear at all (leaving the crew exposed to attack), and had no turret. If you wanted to aim the gun, the driver had to point the tank in the right direction. Some couldn't even elevate or depress the gun, they were so cheap and primitive, though most could and all modern ones do.
They're basically self-propelled anti-tank guns.
Tanks, on the other hand, are designed to combat a wide range of opponents (infantry, other tanks, bunkers, and sometimes even aircraft), have rotating turrets that the main gun is placed in, and are much more heavily armored (or at least, heavy tanks are. Light tanks rely more on speed than armor to keep them alive.).