Well it is in one way. The 123-grain 7,62x39mm bullet can be loaded in the 7,62x53r/7,62x54r full-length cartridge to make a more comfortable and less brutally recoiling load with less flash at night; particularly in Mosin Nagant M38 and M44 carbines.
Just as easily the same .311-.312 bullet can be used in loads for the .303 British, 7,65 Mauser *Argentine* [and Belgian] and 7,7mm Jap, among others. And the .312 hollowpoint bullets meant for the H&R .32 magnum pistol can be loaded into the above cartridges as well; all in the appropriate cartridge cases, of course. There've also been adapters made to allow the use of the 7,62x25mm Tokarev or 7,65 Mauser pistol cartridge in 7,62x54r chambered rifles and some 7,62x39mm weapons for single-shot indoor practice at very reduced ranges; 50 feet or so.
But as a complete loaded round, you're quite correct; they're not at all interchangable.
-archy-/-
The only interchangeability I have found is that the 7.62X51(NATO) round will chamber and fire from the 7.62X54(Russian) Mosin-Nagant. Once.
Extraction is another problem - the Mosin-Nagant requires the uniquely thick rim of the 7.62X54 for the extractor to grab and pull the shell fron the barrel. Also, there appears to be some slight brass swelling on firing.
In fact, the unnamed person I know who tried this ended up having to drive the brass from the chamber from the muzzle end with a ramrod. But this was primarily because the idiot at Sears who sold the rifle ($15.00 for the "sporterized" version circa 1966) included a box of NATO surplus ammo with it. Hell, Dad didn't know the difference (woops!). The gun was never fired again until I figgered out what it was about 1974 and bought the appropriate ammo for it.
That's when I found out Mosin-Nagant was Russian for "big muzzle flash".
Correct, but ours is the 5.56x45, theirs is the 5.45x39. Theirs is basically a 7.62x39 case, necked down to take the smaller bullet. Muzzle velocity and bullet weight are comparable to 5.56X45.