Query from somebody who doesn’t personal an Xbox

I’m shopping for my boyfriend Sonic Generations because it’s my fav sonic sport, and he hasn’t performed it however loves sonic. He has an Xbox 1 which I’ve heard can play 360 video games. So do I’ve to purchase the disc that claims 360 and 1 or does that simply imply the graphics look extra superior if performed on the one? Im sorry if this query is silly or complicated, simply wanting to purchase the 360 one because it’s rather a lot cheaper but when he wouldn’t be capable of play it on the one then I’ll get the opposite.