IMO. Sport allows the wheels to spin in the rear. It is more for drifting and such allowing not so strict traction control. The transmission shifts harder than default but not as hard as Track Mode.
For example I have a custom mode set up for the times when I need a bit more “wiggle room” on the street. Track tranny (most firm shifts), custom traction (least computer resistance), default suspension (softest ride and best for weight transfer to the rear if you need to get out of the way quick). The rest of it, steering (whatever you like) and power (always max for me) are no brainers.