Official Language & Dialects
The official language of Iran is "Persian" but each region has its own
dialect.
"Persia" is what Greek historians called "Parsis" at the time of the
Achaemenids (600 BC). Over the centuries "Persian" was used to refer to the whole Country of Iran and therefore could be used interchangeably with Iranian.
Iran's languages and dialects are mostly derived from Indo-Iranian
languages, which were languages spoken by the Indo-Europeans. The current Persian language belongs to the Iranian branch of Indo-Iranian languages.
The Iranian languages and dialects are radically different from the Arabic or Turkic but were affected by the invasions of 7th and 12th Centuries. Fars and Farsi is the Arabic form of Parsis and Persia. Since Arabs did not have "P" sound, they turned Pars to Fars. But calling the Persian language by the three names of Farsi, Dari and Tajik is quite a recent phenomenon.
Linguists have agreed to call the language of Darius and Cyrus Old Persian, the language of Sassanids, Middle Persian and Iran's present language "Persian", which makes it the grand child of Old Persian and the Child of Middle Persian (Pahlavi). All three stages of Persian language (old, middle and present) belong to The Iranian branch of Indo-Iranian languages.
The current Iranian branch is composed of many languages such as:
1) New Persian (Dari)
2) Assi or Assti which is spoken in the Mountainny regions of Caucausus which were formerly and till mid 1800 parts of Iran
3) Pashtoo which is spoke in Eastern Afghanistan and Northwestern Pakistan
4) Baloochi which is spoken in Balootchistan region and even parts of Turkemenistan
5) Kurdish which is spoken in Kurdish regions of Iran, Turkey and Iraq. It's important to note that this language has kept most of its Iranian roots despite the efforts made by the Turkish and former Iraqi regime to force the Kurds to spouse the Turkish or Arabic languages.