'Briton' is a noun referring to someone from the UK. It is a rarely used word. It is hardly ever used in speech and it is mainly used in newspaper articles reporting on the activities of British people (especially in headlines). 'British' is an adjective referring to someone or something from the UK. You cannot say 'a British' on its own, you have to use it with a noun e.g a British man, a British woman, a British car etc. You can however say 'the British' to refer to people from the UK as a whole, and I guess the reason is that the word 'people' is implied here. So you can say 'British people' or 'the British' when speaking generally about people from the UK.