Caucasian has come to mean white though it's not really a very good or even correct definition, the word caucasian comes from the Caucasius Mountains in Russia which some people consider to be the dividing line between the european continental plate and the asian continental plate. Caucasian or 'Caucasoid' is actually a very broad catagory that refers to physical types found not only in Europe but also the Mediterainian, the Middle East, North Africa and nearby parts of Asia. So it actually covers a LOT of area.
If I wanted to be more accurate about describing my race I'd call myself Nordic and I'd probably call my wife Celtic but we're both fine with white if you'd prefer that. It's really not that big of a deal one way or the other.