Heavy tank
The Char 2C was one of the largest tanks ever produced. At the start of World War II, France and the Soviet Union were the only countries to have inventories of heavy tanks, such as the Char B1, T-35, and KV-1. The Matilda II was designed under the British infantry tank concept which is similar to the heavy tank having thick armor and weighing more than their other tanks. It’s usually separate because they have less firepower with their cruiser tanks (comparable to mediums) at the time having the same main armament but more machine guns. Later war examples were the German Tiger I and II, as well as the Soviet IS series. Note that "heavy" versus "medium" is more a question of tactical roles than weight; the Panther, for example, was a "medium" tank that outweighed most Allied "heavy" tanks.
Tank destroyer battalion (United States)
The first nine units were deployed during the Louisiana Maneuvers of 1941, equipped with towed 37 mm anti-tank guns (the largest gun that could be towed by a jeep) and 75 mm guns mounted on half-tracks (the M3 Gun Motor Carriage), and again in the Carolinas maneuvers that November. Their employment was judged a success—though not without some disgruntled voices in the armored branch arguing that the umpires had rigged the results—and on 27 November, Marshall ordered the establishment of a tank destroyer Tactical Firing Center at Fort Hood, Texas, under Bruce, and the activation of 53 new anti-tank battalions under the command of General Headquarters. The term "tank destroyer" was used from this point on, as it was seen as a more psychologically powerful term. On 3 December, all existing anti-tank battalions were reassigned to General Headquarters and converted to tank destroyer battalions.
The new tank destroyer doctrine was formally stated in Field Manual 18-5, "Tactical Employment, tank destroyer Unit", in June 1942. It laid down a focused doctrine—"There is but one objective of tank destroyer units… the destruction of hostile tanks"—and repeatedly emphasized an offensive, vigorous spirit. Tank destroyer units were expected to be employed as complete battalions, held in reserve and committed at critical points, rather than parceled out as small defensive strongpoints. The emphasis was heavy on mobility, and the ability to outmaneuver the attacking armor; this would feed into vehicle design, and cause the speed of a vehicle to be prioritized over survivability.