Is it simply Spain is using Patatas and the rest of the world is using Papas? What is the distinction?
Besides the right answer from user77086, the present day usage is that "papa" and "patata" are synonyms.
"Papa" is the standard word in most of Latin America, Canary Islands and parts from Andalusia. In the rest of Spain the standard word is "patata" . In some parts of Spain "papa" is used only for chips ("papas fritas") while they use "patata" for the potato as it is.