You read the most amazing stuff on the internet.
"The 7.62x51 being slightly more tapered to facilitate better feeding in fully automatic weapons."
No.
The only real difference is that those fully automatic (and semiautomatic) military weapons have somewhat roomy chambers for reliable operation while hot, dirty, and shooting military ammunition from various sources and doubtful wartime quality.
Savage rifles are rather known for tight chambers and I am not surprised that some indifferent milsurp didn't work.
"It should also be noted for educational purposes that even though they are both 7.62 they have different bore diameters. Soviet 7.62= @.312 Nato 7.62= @ .308."
Fuzzy math.
For real educational purposes, it should be noted that the BORE diameter, 7.62mm = .300", is the same within manufacturing tolerances and national approach to setting them. The MN was once widely known as the "Three Line" rifle, a line being the old term for 1/10".
If you know the difference between "clip" and "magazine", you should know the difference between "bore" and "groove" diameter of a barrel.