According to Enemy at the Gates and one of the Calls of Duty (2?), in certain battles every other Russian soldier got a Mosin-Nagant, and the others carried just ammo, with the instruction to pick up the first guy’s rifle when he inevitably got shot.
I think this might be one of those US distinctions not drawn in the Commonwealth, much as “pistol” means “any handgun” (ie including revolvers) here, instead of “only a semi-automatic handgun” like it does in the USA.
In my multi-decade experience with guns, the understood definition always been select-fire + centrefire cartridge + detachable mag + military issue = assault rifle.
You have to be careful with stories like this. The Russians did treat their own troops a bit more callously than we did, but it has become common, even in supposed non-fiction works, to exaggerate or even fabricate these tales. There were a few times when Russians did face arms shortages and troops were occasionally sent into battle without a rifle, but these things sometimes happen when you are trying to arm a group of men as large as the Russian army. In the movie Enemy at the Gates, every other soldier got a rifle. In the real battle of Stalingrad, there wasn’t a shortage of rifles and every man got one. That scene was complete fiction, though it can be said that it was based a bit on earlier arms shortages that had occurred.
There’s also the often repeated story that when the Russians ran low on parachutes they simply flew their planes low and slow and threw the men out into heavy snow and hoped for the best. That one is also not true.