The new BfA Cooking skill is named differently for the two factions, but the name is the only difference between them. Kul Tiran Cooking is the Alliance version and Zandalari Cooking is the Horde version.
Every BfA cooking recipe has 3 ranks. Higher rank recipes allow you to cook more food for the same materials, and higher rank recipes also give skill points much longer. (the exceptions are the new Feast recipes, you always make one, but it will cost fewer materials)
Some of the Rank 3 recipes are locked behind World Quests.