Here in Australia just using South Devons as an example,a fullblood is an animal that has no outside influence,so the animal is traced directly back to England.
Purebred are graded up animals,unfortunately 4 crosses equates a purebred here in Australlia,in New Zealand I believe it is 5 crosses.
Truthfully there are very few proper full blood cattle in the world. Derived breeds,such as Brangus,Murray Grey,Braford,Brahman,Charbray,Brahmousin,etc cannot be classed as pure or fullblood.
As far as I can see the only Fullblood British cattle ( without US,Canadian Australian etc influence) are Hereford,Angus,Galloway,Devon and South Devon (add to the list if you wish)
The Fullblood Tropicals are Red Sindhi and Sahiwal.
Euros I'm not sure of because of their similarities to a few different types,being bred in different valleys just over the hill from one and other.
Colin