Different CV for applying to university and applying to fellowship?

After reading through all (yes, all) questions in the cv tag, I have a thought that CVs for applying to a position of a university are different to CVs for applying to a fellowship. When applying to a position of a university, the quality of the CV is define by your papers, research experiences, education, etc. While when applying to a fellowship, a good CV is the one can show your leadership, volunteering jobs, etc. Yes, there are some overlapped sections, but these two are not the same. What is your opinion?