Iran is used in political context, while both Iran and Persia are used in cultural context.
The country and vast surrounding lands were known as Persia (derrived from the ancient kingdom of Parsa and the Persian empire) until 1935, when Iran came into international use (though in local use long before that) for the country whose boundaries we see today. The Islamic Republic of Iran was founded in 1979 following the revolution.
Not all Iranians are Persian. The CIA World Factbook for 2011 pins the ethnicity breakdown for Iran at 51 percent Persian, 24 percent Azeri, 8 percent Gilaki and Mazandaran, 7 percent Kurd, 3 percent Arab, 2 percent Lur, 2 percent Baloch, 2 percent Turkmen, and 1 percent other.
The official language of the country is Persian, though locally it is called Farsi.
About 58 percent of Iranians speak Persian or a dialect of Persian, 26 percent speak Turkic and Turkic dialects, 9 percent speak Kurdish, and others speak Luri, Balochi, Arabic, Turkish and other languages.
Persians are not Arabs.