Each tank played a different role in Soviet military strategy which relied heavily on armor. Broadly speaking, there were two 'lines' of tanks, the one beginning with the T-55 and the one beginning with the T-64 (launched in/around those years). Generally speaking (again), the T-55 line was for infantry support while the T-64 was for anti tank combat. When it came out, the T-64 might have been the most advanced tank in the world. It had fantastic optics, stabilizers, automated loaders and all the doohickies (historic term) you could want. It was, however, expensive to produce due to the aforementioned and mostly relegated to elite divisions.

Enter the T-72. The T-72 was an update of the T-62, which in turn was an update of the T-55. The T-72 was not as good as the T-64 in that it lacked many of the auxiliary elements that made the T-64 so good (mainly optics). It was, however, far cheaper to produce than the T-64 and was a good tank in it's own right. So by the 1970's the Soviets had an 'elite' tank in the T-64 and a workhorse tank in the T-72.

As for the T-80 it was more or less a modernization of the T-64. The T-80 was used alongside the T-64 due to financial constraints.

I'd advise you look into the various soviet division categories (There's some stuff in here http://fas.org/irp/doddir/army/fm100-2-3.pdf).

Basically the soviets had several categories of division, with A being the best and B, C, etc being 'worse'. Higher category divisions received better equipment, more training and the divisions themselves opperated at a higher level of readiness during peacetime. Category A divisions might have 80% of max strength during peace, while C or D divisions might expect to have old equipment and only have 50% or less of their strength during peacetime.

As for how this relates to tanks, the soviets from the 60s onwards tended to have two types of tanks. They had more expensive tanks that incorporated more advanced features. The T-64 and T-80 fit these roles. Then there were the cheaper tanks, the T-54/55s, T-62s and T-72s. These tanks were generally more basic, cheaper and were used in greater numbers. Category A divisions might expect to have first pick of those better tanks, while the lower category units might use the cheaper and easier to train on T-62s/72s/55s.

Concurrence between designers and differences in purpose, the same reasons why the USSR fielded the T-34 and KV-1 in 1941-43.

There are two branches, the T-64/80 one and the T-72 one.

First, the T-64 was created in the early 60s as a "game breaker" super high end tank, the first to field an autoloader, composite armor, and it had an awesome 125mm smoothbore gun, whose Western equivalents were only put into service in the early 80s. The T-80 followed the same line, but better, since the T-64 proved its limits in the evolution of the platform. In the same way, it had a great autoloader, composite armor, could shoot guided missiles out of the main gun, had good optics and stabilisation, and had a turbine engine instead of a piston one, which gave it quite an awesome speed and acceleration, at the expense of a monstruous consumption and price. That's the "KV-1" branch for you.

Then, the T-72 was developed, at first as a more reliable T-64 (which had severe reliability issues until later variants - like the KV series), but then began differing a lot from the original vehicle. Although it kept roughly the same shape, the autoloader and 125mm 2A46 gun, it had cheaper optics, suspension, stabilisation, and the composite armor was a simpler, a little bit less efficient but still quite good, variant of the T-64's one. The T-72 was the only one of the three to be adapted for export (T-72M, with T-55 optics and plain rolled steel armor), because it didn't compromise the latest Soviet technology. But as a result, it was much easier and cheaper to make ; it costed three times less more time and money than a T-64 of the same era (T-64A/T-72A) and five times less than a T-80 (T-80B/T-72B).

Then, they were used in different ways. The T-64 and 80 primarily equipped Guards and Shock units (respectively, crack troops and units specialised in heavy assaults) and tank divisions, while the T-72 equipped the tank regiments of motorized and mechanized rifles divisions ; keep in mind that a Soviet Rifles division in the 70s-80s had more tanks than a NATO armored division, and that the USSR had 3-4 times more rifles divisions than armored ones, creating a huge demand for the cheaper T-72 and a much more "niche market" for the high-end, expensive T-64s and later 80s. And that goes without counting the allied countries buying T-72Ms by the hundreds, which forced the USSR to boost even more the T-72 production lines, even with Poland and Czechoslovakia producing the things under license.

Last concept, the USSR had four classes of divisions, classed in four categories : A, B, C, D (or A, B, V, G in Cyrillic), according to their level of equipment and readiness. Cat. A units were 100% active (career soldiers, or conscripts having finished training), able to fight in a matter of hours, and had the best stuff the USSR could produce. THose were some units at the European or Chinese borders of the USSR, plus all the airborne divisions, and all troops stationed in East Germany. Cat. B units were more or less 50-75% active (core of career soldiers, a part of the staff was in reserve and had to be called), able to fight in 24-48 hours, and had quite good stuff, but not the latest. That's a significant part of the Soviet military potential, mainly in "remote" Warsaw Pact countries like Romania or Bulgaria, or deeper inside the Soviet territory. Cat. C units were 25-50% active (small core of old career soldiers, some conscripts in training, staff reserves made of older/smaller/not as healthy conscripts), able to fight within weeks, and had older equipment. These were all stationed inside Soviet territory, and had to be formed and brought to the field of battle. Cat. D units were 10% active (some conscripts whose task was mainly to keep the equipment more or less in shape), were able to fight within a couple months, had to find and (re)train their wartime staff from older soldiers and people in meh health, and were issued with WW2-ish equipment. These were, too, inside the USSR. Their equipment and staff was low-tier, but according to Soviet estimates, should war attrition force the USSR to use Cat. D divisions, the same process would have left NATO or China with just civilian militias and police forces, which could be wiped by men in their 50s and 100-pound guys with glasses using T-34s and Mosin rifles.

Then, when the mid/late 80s arrived, the USSR found itself with three (or, let's say, four) main battle tanks. The T-80 variants (B, BV, U - the other ones are limited series) were in the staff of first line (cat. A) tank divisions. The T-72B/B1 (later variant, with thicker and better composite armor, and sometimes with extra reactive armor tiles) equipped first line rifles divisions. The T-64 variants equipped second line (cat. B) tank divisions. The T-72A was the workhorse of second line rifles divisions.

Then, they still had loads of T-62s, 55s, which were put into modernisation programs until the end of the USSR in order to equip third line (cat. C) divisions and Naval Infantry tank regiments.

Because you can't only have a design bureau and manufacturer with no competition even if there is no market competition like in a communist country. Same reason why Chinese aviation industry in the cold war alternated between Shenyang(J-6,J-8,J-11), and Chendu(J-7,J-10).

Communist arms manufacturers are very specialized, if your plant makes T-72 tanks, then that is all you know how to make. You talking about plant with thousands of workers, plus the entire supply chain, all of the maintenance requirements, training requirements... ... that's a huge amount of political interest in continuing to develop the T-72 line even if the T-80 was better in every way (it wasn't). In comparison to NATO where the big arms companies like Raytheon, Lockhead Martin, General Dynamics, BAE system, etc are all diversified enough to survive the loss a single contract. And in NATO there is a jobs market for the people you lay off from a tank plant as the tank is phased out, in comparison in communist country the government must find somewhere else for these very specialized workers to get retrained and work. And in communist countries they love to locate the important arms plants in the middle of nowhere, because lessons from WWII, so the action of phasing out a tank line would be like a mini genocide on the ground, with thousands of families being forcibly relocated in army trucks.