The U.S. Model 1903 Springfield Rifle replaced the Krag-Jorgensen and was the primary U.S. battle rifle until 1936, when it was replace as the primary battle U.S. battle rifle by the M1 Garand. In 1942 Remington Arms redesigned the 1903 rifle using some stamped parts and designated it the U.S. Model 1903A3.
There is a great lineage of 1903 models that were manufactured from the introduction of the 1903 to the development of the 03A3 rifles, *including but not limited to:

M1903 Rod Bayonet Rifle;
WWI 1903 Rifle;
M1903 Mark 1 Rifle;
M1903A1 Rifle;
Remington M1903 Modified Rifle;
Remington M1903A3 Rifle;
Smith-Corona M1903A3 Rifle.
The 1903A3 was manufactured by both Remington as well as Smith-Corona. The sniper variant based upon the 1903A3 design, the 1903A4, was used during WWII, the Korean War, and in the very early stages of Vietnam.

The primary visible or noticeable (to the laymen/non-collector) physical differences when comparing the 1903 and the 03A3 rifles *includes but is not limited to the following characteristics:

The stock on the 03A3 is plain in appearance when compared to the 1903;
The 03A3 rear sight is not a ladder style sight affixed to the barrel just forward of the receiver, but is instead a small adjustable aperture style sight mounted at the rear of the receiver;
The finish on the 03A3 is parkerized as compared to the blued finish of the 1903;
The 03A3 floor plate cover is not removable, but actually is a part of the stamped (not milled) trigger guard.

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