Native sheep breeds are as you say native to Britain and include Wiltshire Horn. Other countries have their own native breeds.
Traditional breeds are older breed types which were more common until the modern commercial continental (eg texel) and new manufactured breeds (eg Suffolks) came along - they might also be rare but are not necessarily so. They might also be native but again not necessarily so.
Rare breeds may be native, they may be traditional, but there are not many of them and they come under the umbrella of the rare Breeds Survival Trust - the RBST has various categories to define just how rare or endangered a breed is. RBST breeds are not just sheep but cattle, pigs, horses, goats, poultry - all farm livestock.
Primitive breeds tend to be rare, except Shetlands which are not, particularly in Shetland. The primitives are mostly northern shorttailed breeds - Hebridean, Soay, Shetland, Manx Loaghtan, North Ronaldsay, Castlemilk Moorit (which is also a manufactured breed), Icelandic, Gotland and a whole lot of other European breeds. I would also include Herdwicks. Primitive would also apply to many breeds from other countries. They are defined more by their characteristics than anything - self reliant, easy lambers, good defenders of their young, low input, can be shepherded extensively - basically they have not been so influenced by Man that they have lost their wild abilities. There is much discussion as to whether Jacobs can still be called primitive - I would say that in Britain they no longer are, but in the US they are.
It would be interesting to hear from keepers of other livestock species as to which of those might be considered primitive.