At present, the size of bicycle tires mainly follows the European standard ETRTO (European bikeTire gauge Technical Organization) or ISO standards. However, the Old English and French labels are still used in some cases.
Taking 37-622 as an example, according to ETRTO standards, the bicycle tire width is 37mm and the tire inner diameter is 622mm.
The inch mark (e.g. 28 x 1.40) indicates that the outside diameter of the bicyle tire is 28 inches and the tire width is 1.40 inches. Another common notation is 28 x 1 5/8 x 1 3/8, which roughly represents the outside diameter, tire height, and bicycle tire width.
It is important to note that inch measurements are not very precise. For example, tires with a diameter of 559mm (mountain bike), 571mm (triathlon) and 590mm (station wagon) are all classified as 26 inches. Both 622mm and 635mm diameter tires are defined as 28 inches. Even weirder, a tire with an inner diameter of 630mm is defined as 27 inches.
These definitions stem from the era of bicyle tire brake pads, when the exact outside diameter of a tire was determined by the brake pads. A variety of inner diameters are defined according to different bicyle tire widths.