It's possible that the gun is not chambered for 38 special, but for something else. It may not be an accident that this barrel is marked for 38 MIL.
If I were you, I would try chambering a 38 special cartridge. If it doesn't chamber properly, meaning that it will not seat all the way down in the cylinder, then maybe the gun really is chambered for 38 long Colt. If this is the case, then it might have been a special order, and be important in some way or other.
If it does properly seat a 38 special cartridge, look down the cylinder chambers and see if there is a double ring, which would indicate the the chambers were originally for 38 Long Colt, but were later lengthened for 38 special.
Regards, Mike Priwer