In common use, not much, in fact on the web I just use white because the point is pretty clear.

But if I have to be more philosophical and analitical, the category of "white" was indeed a British colonial semi-invention (it was occasionally used before but in a very limited way, the point was more about moors Vs Christians) that organize in a hierarchical way races and ethnicities. There is the assumption, for example, that if there is a white race, even within the race those who are more white are more pure. So if I say European, or I refer to a particular ethnicity, it's clear that I am talking about a group, with racial, historical, spiritual and cultural characteristics that are concurrent in creating an identity; if I say white I'm speaking about a hierarchical order based on colours.