The original rifle was indeed called the Pattern 1913. It was chambered for the .276 Enfield, which was designed to carry a heavy powder charge and had a very large (.528") base. The deep magazine was needed to hold 5 rounds of that cartridge. When WWI loomed, the British abandoned the idea of changing caliber and reworked the rifle to use the rimmed .303 British. The new rifle was called the Pattern 1914, and due to the rimmed cases, the magazine also held only 5 rounds. Some were made at Enfield, but when war came the British decided to concentrate British industry on the SMLE Mk III, for which tooling already existed, and farm the Pattern 1914 out to American manufacturers under contract.
When the U.S. entered the war, the companies (Winchester, Remington, and the Remington-managed Eddystone factory) had just completed the British contracts, but were asked by the U.S. Army to adapt the Pattern 1914 (P.14) to the U.S. .30-'06 cartridge. This was done, and most of the rifles used by American troops in WWI were the modified P.14, dubbed the U.S. Rifle, Model of 1917. Due to the fact that the .30 caliber was rimless, the large magazine would hold six cartridges, though it was always loaded with 5-round clips, the same as were used with the Model 1903 Springfield.
In the common usage, the modified British rifle, the Model of 1917, was always called "the Enfield", while the native American Model 1903 was always called "the Springfield", and many were the arguments (still going on nearly a century later) over which was the better rifle. A realistic conclusion would be that they were both darned good.
Jim
