Cities are bigger than towns.
Towns are bigger than villages.
Villages are bigger than hamlets.
As hinted at above, in the United Kingdom,, a place is only a city if it has official city status. This comes in a variety of ways. Traditionally seats of dioceses of the Church of England are cities, but this is not always the case and city status can be given for other reasons. The Church of Scotland does not have bishops or dioceses so this does not apply in Scotland. In recent years the Queen has given towns city status to celebrate important anniversaries, about the only modern use of the Royal Prerogative that is not on the advice of the Prime Minister. Generally cities are bigger than towns, but St David's, in Wales is a city but has a population of about 3000, and there are towns withe populations of hundreds of thousands. There is a good Wikipedia article on City Status in the United Kingdom.
