Basically, I've always understood the word "sport" (as related to animals and plants) as a spontaneous, unrelated genetic mutation that has appeared in a population or as an offshoot. For whatever reason, the gene has appeared and has nothing to do with the parent(s) genetic makeup, meaning there was no way they could have contributed to the new quality the offspring has.
As far as chickens go, I know the splash version of fawn in OEGB is called a "sport", but since it's an established color, I don't know why it's called this. I do know that blue Jersey Giants are the result of a spotted sport that popped up in Gold Miller's white flock way back, so no outside breed was used to bring blue into the blue breed.