The 303 British and 303 Savage are two different cartridges. The 303 British was developed in Britain, while the 303 Savage was developed in the United States. Both cartridges are very similar, but there are some differences.
The 303 British is a rimmed cartridge that uses a large rifle primer. It has a case length of 2.22 inches (56mm) and an overall length of 3.26 inches (83mm). The bullet diameter is .311 inches (7.9mm). The maximum pressure for the cartridge is 50,000 psi (345 MPa).
The 303 Savage is a rimless cartridge that uses a small rifle primer. It has a case length of 2.19 inches (55mm) and an overall length of 3.23 inches (82mm). The bullet diameter is .308 inches (7.8mm). The maximum pressure for the cartridge is 45,000 psi (310 MPa).
Both cartridges can be used in rifles chambered for the other cartridge, but there may be some issues with feeding and chambering due to the different case sizes and shapes.