2 calibers in one
I've just done the math, and 7.62mm does not equal .308". Nor does it equal .311". These designations are done arbitrarily, for a variety of reasons, and make a fascinating historical study, if you have the time and the inclination. But your question was, why have 2 different calibers designated 7.62x39mm.
Russian military designers thoughtÑfor whatever reasonÑthat .311" was a nice diameter for their 7.62 rifle barrels when they designed the so-called 7.62x39mm round. (They whould have used a metric measurement for this however.) That round went through the various SKS models, and the various AK models, the latest of which are still in use. The same standard was used by the Chinese, and the other nations to which the USSR/Russia exported weapons-building technology, from the 1950's through the 1990's. So there are lots and lots of old military weapons designated 7.62x39mm, with this bbl diameter.
When Ruger subsequently decided to chamber their Mini 30 in this round, in their infinite wisdom, they chose to make the bbl. diameter .308", for whatever reason. Perhaps because other cartridges popular in this country, which are called 7.62mm elsewhere, are .308" diameter. Notably the .308 win, aka the 7.62 NATO. I'm not representing this as good logic, you understand, but it's what Ruger did.
So from two different sources, you have the same round with 2 different diameters.
A potentially dangerous situation.
If you had a .308" diam. 7.62x39mm bbl, and fired the .311" diam ammo in it, the best you could hope for would be a ferocious kick and lousy accuracy, as the large bullet is violently forced to conform to the smaller bbl. Internal pressures would be I think, dangerously high. Gun damage and damage to shooter or bystanders are worse case scenarios. So you would be well advised to stick with domestic American sporting rounds, which are .308" diam.
If, OTOH, as you say you have, a .311 diam bbl, you should be seeking and using .311" diam bullets. The .308 diam bullets will probably upset (flatten their back ends) in the barrel and seal the bore, but they will probably NOT do so pointing straight down the bore, which means they will be headed God-knows-where when they exit the muzzle. Not a dangerous situation, but highly inaccurate, and not predictably so. If the bullets always went left of point of aim for example, you could adjust your point of aim, but when they upset in the bore they may be pointing left, right, up, down, or straight ahead. If the bullets don't upset, they'll just rattle down the bbl, with pretty much the same result as above, except with less velocity due to blow-by of some of the powder gases.
Bullets of both diameters can be had easily by reloaders, so there is no excuse in either case not to have high quality ammo for your weapon. Accurate Arms 1680 powder was designed specifically for this round, and usually works well. It seems to be the logical place to start in load development for a particular weapon.
IMHO, you have hit the proverbial nail on the head.
But that's just me. I wonder if this is one of those cases where "that's the great thing about standards, there are so many of them !!"
Nice way of putting it.
BTW, since you have a .311 "7.62x39mm", I hope you enjoy shooting your milsurp.