My Great Grandfather and his family listed Hungary as place of Origin in the 1910 census, but list Austria in the 1920 census. Can anyone explain?
Which town are you talking about? Austria-Hungary existed until the end of the First World War. Following that there were separate countries of Austria and Hungary.
Yes, although Hungary was a well-defined part of the Austro-Hungarian Empire. There was some territory (the Burgenland) that was part of Hungary before the war and became part of Austria after the war. However, it may be reading too much into this to suggest that as the explanation.