In the games the Galar League will be special in the sense it's gonna be a tournament for the guys who got the 8 badges (like the anime) and the winner gets the chance to battle the champion and take his title
In the anime the Galar League will be special in the sense it's gonna be the Champion tournament Cynthia mentioned and as most recent Champion Ash is gonna be requested to meet and recruit the champions of the other regions for the league in Galar