meaning - "all" vs "both"

I am wondering whether "all" and "both" mean exactly the same.

I always use "both" to refer to explicitly two things, like

Red and orange both are my favorite colors.

As for "all", I would only use it when the number of things is more than or equal to three, like

All China, Japan, Korea are Asian countries.

My friends told me that "both" and "all" have actually the same meaning, so could anyone give me some suggestions?

Thank you!