Except for a little difference in length(and that is not very much)the case dimensions for both cartridges are the same, within a couple thousanths,so the difference would be determined by "slugging"the barrel to determine groove diameter.If it is .375-.380" it is 380 Long,if .357-.362", it is 360#5. A .378-380" bullet is practically the same as the neck diameter of .379", so it would have to be a heeled bullet. The smaller bullet is significantly smaller and could fit into the case. I have found that the 360#5 is often confused with one of the 360 Express cartridges(usually 360 2 1/4") and listed as having that cartridges bullet diameter. I wish I had a double handfull of both caliber rifles and Ammo for them. Then maybe I could give a definitive answer, but until then my opinion is not worth any more than anyone else's.
Mike