No good reason. 7.62 mm converts to .300" which is the bore diameter of the 7.62 NATO, .30-'06, etc. .308" is the groove diameter. Why the Russians chose a bit larger bullet and why they called it 7.62mm (instead of, say, 7.7mm/.303"), I have no idea and I doubt anyone does at this stage.
I do happen to know why .30 was chosen by the U.S., though. Around 1890, when the Army was experimenting with reducing the standard rifle caliber from .45 to something smaller, an officer at Frankford Arsenal decided to use .30 (.308), thus setting the standard U.S. rifle caliber for the next 75 years. When asked why he chose .30, he replied that "it seemed like a nice round number."
Thus are decisions made.
Jim
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