I acquired a savage 116 .338 and was given a container of shells that were apparently shot through the rifle. They say 300 win mag. I don't know much about the rifle but can a 300 win mag be shot through a 338 win mag?
No they can not. Someone gave you the wrong ammo or resized 300win to 338 win but since I don't reload either caliber im not sure if that's even possible. Only fire what is printed on tje barrell or the consequences could be drastic.
It will be easy to tell if they were fired from your rifle, try to chamber one of the spent cartridges. If it will chamber then the brass has been resized to .338 Win by someone who reloads. Both cartridges head space off the shoulder as well as the belt. A .300 Win Mag will not chamber in a .338 rifle because the shoulder on the .300 Win is moved forward. If you ever start reloading you can use the brass to reload for the .338, or if it hasn't been resized you always can trade them for .338 brass.