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.
Main battle tank
A main battle tank (MBT), also known as a battle tank or universal tank, is a tank that fills the armor-protected direct fire and maneuver role of many modern armies. Cold War-era development of more powerful engines, better suspension systems and lighter weight composite armor allowed a tank to have the firepower of a super-heavy tank, armor protection of a heavy tank, and mobility of a light tank all in a package with the weight of a medium tank. Through the 1960s, the MBT replaced almost all other tanks, leaving only some specialist roles to be filled by lighter designs or other types of armored fighting vehicles.