Why do certain notations differ around the world?

You see, it depends mostly on culture and translation, and also the habits. When you get used to using a notation you cannot give up on it easily. For instance, the notations you gave for derivates are both acceptable. If I am right, one of them is the notation used by Leibniz, and one of them by Newton. They can both be used and whichever comes easy, you use it. However, the upperline notation is a different case. For instance, in my country we use that as you do too, and I guess it is used in every country but it is not so popular you see. The notation itself is usually used (also in my country) in mathematical olympiads. Also if you want to learn more, I suggest you reading this article https://www.stephenwolfram.com/publications/mathematical-notation-past-future/.