To me, ethnic means the group of people you have descended from. The culture, traditions, history, looks that have been passed down to me from generations ago are all part of my ethnic heritage. Most of us "white" people prefer to be called "European Americans" or (some of us) "Anglo Saxons". The term Caucasian would be ones who came from the Caucasus regions:
The Caucasus is one of the most linguistically and culturally diverse regions on Earth. The nation states that comprise the Caucasus today are the post-Soviet states Georgia, Armenia, and Azerbaijan. The Russian divisions include Krasnodar Krai, Stavropol Krai, and the autonomous republics of Adygea, Karachay-Cherkessia, Kabardino-Balkaria, North Ossetia, Ingushetia, Chechnya, and Dagestan. Three territories in the region claim independence but are not universally acknowledged as nation-states by the international community: Abkhazia, Nagorno-Karabakh and South Ossetia.
None of my ancestors came from those areas and I doubt if many "whites" in America have ancestors from those regions.
So - therefore, I think I am saying to me ethnic means heritage.