No they are far from the same cartridge. The savage is slightly shorter than a 308 Winchester, which is a "short action" cartridge, and holds slightly less powder. Ballistics are near identacle.

The 300 Win Mag is a "long action" magnum based on the H&H case design. It is a belted cartridge which far exceeds the ballistics of the Savage or .308 Win.



300 Savage left, 308 Win. right, 300 Win mag far right.
No the two pics are not to scale but you can see the case differances.