It can be both depending on the context. A westerner is a european or a european descended person.
> For example many Asian people are more western than many white Americans.
What does this even mean? How can an asian person be more western than a white american. That's like saying a white american be more "eastern" than a chinese person.
I've never heard an asian person say they are a westerner. There may be asian people who appreciate western culture more than some westerners, but that doesn't make them a westerner. No more than a white american who appreciates chinese culture more than the average chinese makes him a chinese person.
Or are we talking about different things here?