Working Cockers are 'Cocker Spaniels' ... working Cockers and show Cockers are two types or strains of the same breed - they are different in looks and usually in character/traits but they are both classed as Cocker Spaniels.
I don't know of any responsible breeder who would combine the two strains though, there is not really any good reason to do so. The aim of any good breeder of either strain should be to improve the breed and this is not going to be achieved by crossing working and show Cockers, you're not going to produce better show dogs or better working dogs by doing this and there are already too many dogs out there - including Cockers, just look at the rescue board on this forum - so it's hard to justify breeding more purely as pets, particularly when they do not do anything for the breed as a whole. It does happen but generally is done either by people who do not know, or do not care, what they're doing; or by commercial breeders and puppy farmers who are breeding dogs purely for profit and don't care what dogs they use.