IIRC, the term came from the British, who had "Infantry Tanks" (slow, heavily armored, tended to have a small gun) and "Cruiser Tanks" (fast and lightly armored). The MBT was supposed to have the armor of an Infantry Tank but the speed of a Cruiser.
The British had some really weird tank classifications
Early on, the question was whether to keep the tanks slow enough that the infantry could keep up on the walk, or whether to make the infantry faster via armored transport. The British actually built both ideas. The Infantry tanks, especially the Churchill, were geared low enough that they could go just about anywhere a man on foot could.
I understand what the British were trying to do but I find it interesting that their iron triangle for certain classes looks different, I also find it funny that we’re talking about this at 2am.
The iron triangle is already quite simplistic on its own, but is even less applicable to most tanks of WW2. It's more of a post-hoc explanation by pop historians.
In reality, engineers often just selected their own bespoke components and layouts without trying to adjust parameters on a single shared platform. And different classes did not always have identical weight limits where trading only propulsion, protection and firepower at equivalent weight is valid.
Except in the US where designing was mostly concentrated in a single group with most outliers never entering service, different tank classes were the result of competing factions in military services, or were designed by very different companies, which resulted in few vehicles adhering to shared optimal design practices and components to adjust the iron triangle around.
For example, the Matilda II and Cruisers were the result of a disagreement between military factions as to whether heavy armor would be necessary and viable or whether speed only should be emphasized. The Matilda was designed prior to the Cruisers and shared ideas with the previous A7E3 medium tank, so had twin engines and a conservative coil spring bogie suspension while the Cruisers moved on straight to a more weight and volume efficient single high power engine, and a suspension which was more weight efficient and capable of higher speeds. The uparmoring studies done for the Crusader show that it could have gotten quite close to Matilda II at a lower or identical weight if needed, while still being more mobile. Indeed what 1940 showed was that you couldn't get away with light armor.
In the USSR, the KV and T-34 tanks were designed independently with the latter lacking the more efficient torsion bar suspension of the former, but having a more weight efficient arrangement of the front armor and rear plate.
It is only late in the war that designs start to converge in single platforms, such as how the A27 Cruiser tank and A33 Assault tank share a similar layout, armament and powertrain. Even then, heavily armored vehicles are just heavier instead of applying the iron triangle as we generally portray it. More often than not, the actual tradeoff is with the weight and ease of transportation.
Even then, as long as tanks didn't reach maximum logistical limits, there was still room to make the universal tanks that were needed. The appearance of the MBT has a lot to do with the fact that countries finally put a lot of effort in a single tank and gave them decent limits on weight and dimensions.