Matter of preference, but here's my take: "Main battle tank" is a role, and an ill-defined one at that. "Heavy tank" is a weight class. Also one man's meat is another's... appetiser I guess; different countries' "MBTs" are of different weight classes. So I prefer using the latter :D
Just some very broad stroke background info on tanks, when they first came out you had male and female tanks (depending on if they had cannons or MG for their main guns). Later they started calling them light (some called them tankettes) and heavy but if you ask me that was more to do with size/role then truly weight based. After WWI they keep working of different tank designs and roles for them.
So around the start of WWII there was the standards designations of cruiser tank, infantry tank, anti-tank "tank" (tank destroyer), assault gun. The Cruiser Tank was a modern version of the Cavalry, they would break through the enemy lines and attack the lines of communications. They were generally lightly armored but for the time fast, with some firepower but geared to taking on unarmored to lightly armored support units only. The infantry tank was generally heavily armored but slow (some with a top speed full out of 8mph) they had good firepower but was designed to support the infantry in the assault. The tank destroyer was just as you would guess from its name designed to destroy tanks, so it has a good anti-tank gun most were fast to very fast with light to very light armor (most were also open topped) intended to attack from cover and ambush. The assault gun is very much like the infantry tank, but with out the turret were generally more mobile. They also were mostly used with larger rounds and used HE rounds and could fire directly and indirectly. As the war progressed the cruiser tank became light/medium tanks, the Infantry tank became the medium/heavy tanks, and towards the end of the war you even saw some super-heavy tanks. At this point tanks started to become more multi-role but the weight class had more to do with what part of the speed/firepower/armor was on top, you still had tank destroyers and assault guns but they were being used less and less for the mission they were intended and more the same as the general purpose tanks.
Post WWII up to modern time the trend of multipurpose tanks with the weight classes being used less and less eventually medium and larger being replaced with Main Battle Tank (MBT). Just some interesting numbers light tanks lightest that I could find came in at 1.5 tons combat loaded, to heaviest at 35 tons. Medium tanks lightest 14 tons, heaviest 42 tons. Heavy tanks lightest from 28 tons, heaviest 76.9. And just for fun super-heavy tanks lightest from 60 tons, heaviest produced (Maus) 188 tons, heaviest that had plans drawn up (Landkreuzer P. 1000 Ratte) at 1000 tons. So as can be seen there is a fair amount of cross over when using weight as the classification, I think this is mostly as technology improved you can get better performance so you can go bigger and still have the same performance that you had with more armor and/or firepower. Now using the MBT term weight does not come into it as it is based on the role it is designed to do.
