Does it have a J lock on the bolt? They all did originally, but its an easy change, so may have already been swapped out. The contour from the shank is also a bit different (at least on the 300 and 338's). If an original AWR, they are awesome rifles, as were the KS versions. I have had several and still own a KS and a AWR, both in 338. Oh, and same in the Model 7, that one is a 7mm SAUM.
It will not have all the markings of the regular Remington scrolled down the barrel. I cannot remember what all there is, but can look tonight if still needing to know, just PM me.