Amateur here, but this is how I imagine it:
Light tanks are for giving motorized and mechanized divisions an extra punch, or for invading/defending countries that lack the industrial capacity for armored units. When you think "Blitzkrieg", these are the speed demons you think of.
Medium tanks are a nice mix of speed and firepower, good for a slower-than-average motorized/mechanized, good for pushing breakthroughs. A jack-of-all trades that can perform most tasks adequately, and provide nice support for your unarmored units.
Heavy tanks are for invading countries that will absolutely have a lot of tanks and men, where you need something strong to make short work of infantry while standing up to enemy armored divisions. Heavy tanks also make good defenders, acting as a sort of mobile low-level fort that can defend vital choke points.
Superheavy tanks are for when you just say "FORNICATE IT", throw logistics, industry, practicality, and basic human intelligence to the wind, build a tank the size of your capitol building, and then wonder why you're suddenly out of fuel, all the roads have been destroyed, and the enemy air force is suddenly so excited.