Persian (Iranian) people in the English-speaking countries are the only community who use two different terms to refer to their language, “Farsi” and “Persian.” This behavior has caused some confusion among the Westerners as to the appropriateness of these terms.

“Farsi” (an Arabic adaptation of the word “Parsi”), is the indigenous name of the Persian language. Just as the German speaking people refer to their language as ‘Deutsch’, the Greek ‘Ellinika’ and the Spanish ‘Espanol’, the Persians use ‘Farsi’ or ‘Parsi’ to identify their native form of verbal communication.

In English, however, this language has always been known as “Persian” (‘Persane’ in French and ‘Persisch’ in German’). But many Persians migrating to the West (particularly to the USA) after the 1979 revolution continued to use ‘Farsi’ to identify their language in English and the word became commonplace in English-speaking countries.



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Note added at 12 mins (2009-01-30 07:26:52 GMT)
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http://heritage.chn.ir/en/Article/?id=88

The term Persian has been used in the English language for over five hundred years: to describe both a nation with 7000 years of archaeological history, and also the language that nation has used since the rise of the first Persian Empire, the Achaemenids.
Unfortunately however, the word ‘Farsi’ is increasingly and incorrectly being used to describe the Persian language.
http://www.cais-soas.com/CAIS/Languages/persian_not_farsi.ht...

So, both 'english to farsi' and 'english to persian' mean: انگلیسی به فارسی