What are the various sizes of cables and their uses?

Massive of range of cables. Generally speaking lighting 1.5mm cable. Power 2.5mm cable. Anything feeding an appliance up to about 9.5kw 6.0mm cable. Above that 10.0mm cable. Domestic feed 25.0mm cable (16.0mm earth) hundreds of different supply and demand sizes. Refer to bs7671 17th edition for more information.