U.S. Magazine Rifle
   Model of 1896
   Model of 1898
   Model of 1903
   Model of 1917
THE U.S. Magazine Rifle followed by Model number (year). It does not appear that the "Model" number appears on the receiver of the rifle until the "Model 1896" came along. To this end, and this is just my opinion without a lot to base it on, when the term "U.S. Magazine Rifle" was used it meant the adopted Krag Jorgensen rifle starting with the Model 1892 and including all the variants up to the Model 1896. It was the only "U.S. Magazine Rifle" fully adopted, was it not? Once there was a Model 1896, Model 1898, etc, then things had to be better distinguished.
Drop the U.S. from "U.S. Magazine Rifle" and then I believe things get less descriptive, although it may have been understood at the time between like-minded people what they were talking about.