Great Britain is the island that England, Scotland and Wales are on. It’s a purely geographical term, not political.
The UK is the United Kingdom of Great Britain and Northern Ireland.
The British Isles are Great Britain, Ireland and the smaller islands (Isle of Man, Channel Islands) that constitute the archipelago. You have to be careful with that one, as it’s obviously not generally a popular usage in the Republic of Ireland.
I don’t think Britain has a specific meaning. Usually refers to either GB or UK.
