The White ones are game chickens and the ones with brown are game chickens mixes.
If you get an assortment of pure breeds from a breeder and have a list of the breeds they gave you then it is safe to assume they are pure breed if not...well they really probably aren't a breed at all. Most of the utility birds and hatchery birds are mixes that are created by crossing breeds but are not a breed them self. A breed is something that has been inbreed for many many generation and never breed to anything out side the family. This leads to them being able to produce only the specific traits that the breed was developed for. The Leghorn's specific traits are White Eggs, Yellow Skin, Single comb, white ear lobes, etc. Yes... the white ones lay white eggs, yes, they have a single comb, but I am not seeing white ear lobes, and the skin looks white, so these don't look like Leghorns to me. The Old English Game breed's specific traits are White Eggs, White skin, Single comb, red ear lobes. This would be closer the Game that you were told that they were, but if you don' know what they are, then then go back and ask the person you got them from because there are so many mixes out there that if you don't know for sure that they are a pure breed they most likely aren't.