Farsi is to Persian
as Français is to French
Farsi deserves a node of its own because in recent years it has become interchangeable with 'Persian' when referring to that language by non-native speakers. Even though some Iranian authorities encourage the official adoption of this term by other countries, its usage offends others who feel that it ignores the history of the language and avoids the positive cultural associations that Persian has.
Although it was originally widespread throughout the Persian Empire, today the language is most common in Iran and Afghanistan. Worldwide it has over 30 million speakers.