What are the differences among the Salat al-Sunnah, Salat al-Tatawwu and Salat al-Nafil?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

It is said that As-Sunnah, Al-Tatawwu' and An-Nafil prayers are identical. It is also said that they have slight differences.

Al-'Iraqi wrote in his book entitled "Tarh at-Tathreeb": "The known opinion of Ash-Shaafi'i School is that At-Tatawwu' is what the Sharee'ah considers better to be done than to be left, although neglecting it is permissible. Therefore, At-Tatawwu', As-Sunnah, Al-Mustahab, Al-Mandoob and An-Naafilah are all synonymous according to them."

However, some other Shaafi'i scholars differentiated between the above technical words. Al-'Iraqi aslo wrote in the above book: "Other than the obligatory prayer, there are three kinds (of acts or prayers): As-Sunnah, which means those acts that are frequently practiced  by the Prophet ; Mustahab, are those acts the Prophet performed occasionally but not regularly; At-Tatawwu' means the good acts a person performs by himself without having any specific evidence for that from the Sharee'ah."

However, the Maaliki School differentiated between As-Sunnah and Al-Fadheelah (merit, virtue).  As-Sunnah, according to them are actions that were performed by the Prophet regularly and publicly.  And the actions he did not perform regularly are called al-Fadheelah (merits).  The actions he did regularly but not in public such as the two Sunnah Rak'ahs of Fajr, they can either be called Fadheelah or Sunnah.

Allaah Knows best.