A couple of comments. It was the British custom in that era to name its military rifles after the inventor (James Paris Lee, in this case) along with the type of rifling used. Hence, the Martini-Henry, Martini-Metford, Lee-Metford and Lee-Enfield.
The original Lee used Metford rifling and was designated the Lee-Metford. When Metford rifling proved unsatisfactory, the Lee-Enfield came into use, employing rifling developed at the RSAF, Enfield Lock.
But they also wanted to distinguish the Lee rifle, a repeater, from the older Martini rifle, a single shot, so they added the word "magazine" to the Lee-Metford name, creating the name "Magazine Lee-Metford" or MLM. That designation continued into the LE era, so the long rifle was the Magazine Lee-Enfield, or MLE.
When the British decided to join the rest of the world in adopting a common intermediate length rifle to replace the long infantry rifle and the short cavalry carbine, they added the word "short" to the nomenclature, giving us the immortal "SMLE" or "Smelly". So, contrary to the belief of some, it is the rifle itself that is "short", not the magazine.
For Americans, it might help to imagine the use of commas as our military does, and think of the designation as "Rifle, Short, Magazine, Lee-Enfield."
Jim