Sizes
The chain in use on modern bicycles has a 1/2" (=12.7 mm) pitch, which is ANSI standard #40, where the 4 in "#40" indicates the pitch of the chain in eighths of an inch, and metric #8, where the 8 indicates the pitch in sixteenths of an inch.
Shimano did make their own 10 pitch system with 10 mm pitch from about 1970 to 1980 - called Shimano 10 pitch. The Shimano 10 pitch system is incompatible with ANSI standard #40 (1/2") e.g. chains, sprockets and so on.
Width
Chains come in either 3/32", 1/8", 5/32", or 3/16" roller widths, the internal width between the inner plates. 1/8" chains are used on bikes with a single rear sprocket: those with coaster brakes, hub gears, fixed gears such as track bicycles, or BMX bikes. Chains with 3/32" wide rollers are used on bikes with derailleurs such as racing, touring, and mountain bikes. Fixed sprockets and freewheels are also available in 3/32" widths so fixed-gear and single-speed bikes can be set up to use narrow and lighter 3/32" chains. Finally, chains with 5/32" wide rollers are used on freight bicycles and tricycles.
With derailleur equipped bicycles, the external width of the chain also matters, because chains must not be too wide for the cogset or they will rub on the next larger sprocket or too narrow that they might fall between two sprockets. Chains can also be identified by the number of rear sprockets they can support, anywhere from 3 to 11, and the list below enables measuring a chain of unknown origin to determine its suitability.
06 speed - 7.8mm (all brands)
07 speed - 7.3mm (all brands)
08 speed - 7.1mm (all brands)
09 speed - 6.6 to 6.8mm (all brands)
10 speed - 6.2mm (Shimano, Campagnolo)
10 speed (Narrow) - 5.88mm (Campagnolo, KMC)
10 speed (Narrow, Direction) - 5.88mm (Shimano CN-5700,CN-6700,CN-7900)
11 speed - 5.5mm (Campagnolo, KMC, Shimano CN-9000)