In and around Washington, D.C., there exists a large community of individuals who left Iran during and immediately after the 1979 Islamic Revolution, most of them because they were closely associated with the regime of the deposed Shah. If you are smart, you will never, ever refer to these people as Iranians. They are Persian, damn proud to be Persian, and those of the older generation may pretend to not even know what an Iranian is.
Not all of the members of the Persian community are even still particularly attached to the legitimist cause, but they are still quite adamant about being Persian and not Iranian.