Cochin, old english, silkie, dorking, leghorn, orpington, etc are breeds. Conformation and size of the bird, as well as many other characteristics make the breed,
Variety is colour/colour pattern: blue, splash, partridge, birchen, silver duckwing, BBR, etc. Almost all breeds come in multiple varieties, and most varieties occur in multiple breeds, THere are many breeds of red chickens, blue chickens, partridge chickens, silver duckwing chickens etc. Likewise, orpingtons come in buff, white, black, blue; old english come in fawn silver duckwing, black, splash, opal, BBR; araucana come in silver duckwing, black, white, blue; etc.