http://www.lao.ca.gov/publications/report/3724 says that, for California public schools, “Whereas CCC defines students as first generation if neither parent has ever attended college, the CSU and UC definition is that neither parent has earned a bachelor’s degree.” (CCC = California community colleges) Note that there is no exclusion for college attendance or bachelor’s degree earning outside of the US in this definition.
So yes, it can vary depending on the college.
It can also vary as to whether it makes a difference in admission to the college. It obviously does not for the community colleges, since they are open admission (though a community college may offer services specifically helpful to first generation students who are likely to be less familiar with college than other students).