To be accurate, those identifying themselves as Persians do this to distance themselves from the "official" Iranians (speak islamists). This is a post-1979 phenomenon and understandable. However before 1979 (and BTW the accurate description) is Iranian, since Persians are only a segment (albeit the largest) of the Iranian people, which include the Kurds, Azeris, Dari etc. Irani is also the native word for Persians, just as Iran was since millenia for the country, althout the West called them Persia. The nationalistic, patriotic minded folks under Reza Shah therefore insisted on the world calling them Iran instead of Persia. Iranian was the modern, secular and patriotic slogan of the hour, while Persian was equated with backwards, superstitous, fanatic and dependent. Ironic that the usage of words was twisted after 1979.