Yeah, I think the word "shuffle" itself indicates what people are actually looking for here; when I shuffle a deck of playing cards, I'm changing the order, but

Yeah, I think the word "shuffle" itself indicates what people are actually looking for here; when I shuffle a deck of playing cards, I'm changing the order, but I'm still getting every card exactly once when I deal them. Nobody claims that the deck order isn't random because you can't get the 7 of clubs twice after shuffling it.