The term bore refers to the hollow internal diameter of the gun barrel. Technically this applies to all weapons. In everyday usage, especially in countries like India, it is commonly used as a general term for the size of a weapon. Like people often say 32 bore revolver and 45 bore pistol.

Caliber is a precise measurement. It is used for rifles, pistols and revolvers. It tells you the internal diameter of the barrel and the size of the bullet fired from it. Caliber is stated in inches or millimeters.