There are several different types of commonly used water supply pipe that you may have. These may be copper, plastic or MDPE (there is lead also but as you would expect it is no longer used, but on occasions you may still need to connect to an existing lead water network, where converters are available to MDPE and copper)
Looking at copper first of all, there are metric and imperial sizes. Metric sizes are measured using the outside diameter, i.e. the outside diameter is either 8mm, 10mm, 12mm, 15mm, 22mm, 28mm, 35mm, 42mm and so on. Imperial sizes are measured using the approximate bore diameter, for instance the outside diameter of 1/2" copper pipe is about 15mm and 3/4" is about 22mm and 28mm is about 1 inch in diameter. This is where errors are often made, confusing metric with imperial water pipe. For instance 15mm and 1/2 inch water pipe (and 3/4 inch and 22mm) are virtually indistinguishable in size, but it is still critical to use the correct fitting, particularly with end feed fittings as you will not good a good solder capillary action with a poor fitting tolerance. Imperial to metric converters are available from most good plumbing merchants of by searching "imperial" here to join the two types of pipe.
Plastic pipe sizes are less of a challenge and are only available in basic metric sizes, mainly 10mm, 15mm, 22mm and 28mm, measured by the outside diameter. Fittings are available for these fittings which can be used to fit to their copper counterparts. So a 15mm pipe can be joined to a 15mm plastic pipe using a 15mm push fit or 15mm compression fitting. Note here though that a pipe support or insert should be used in the end of the plastic pipe to give the fitting some strength and protect the fitting from blowing off. Most plastic pipes of this style are white (or grey) in colour and come in two variations, Polybutylene pipe (PB) which lays flat when uncoiled and is more flexible than the alternative Polyethylene (PEX) Pipe, which when uncoiled retains its coil shape, so can be difficult to work with, particularly when pulling through tight spaces. In addition plastic water pipe come in standard format and barrier pipe format where barrier pipe is designed to be used in central heating systems specifically, as it incorporates an oxygen barrier to inhibit oxygen permeation, reducing the risk of corrosion
MDPE water pipe is blue in colour and is general used outdoors, often underground, to provide a supply to a building or complex. MDPE is Medium Density Polyethylene. There are push fit and compression fittings available, with compression versions available in brass (or brass DZR for corrosion resistance) or plastic. A pipe liner or insert should be used to give the pipe support, preventing the fitting from blowing off the pipe. MDPE pipe sizes are generally 20mm, 25mm, 32mm, 50mm and 63mm and MDPE conversion fittings can be used to connect all sizes to copper, plastic or lead and are available here