Is the obligatory prayer the Fajr prayer or the Subh prayer, and is it correct to pray Fajr as an obligatory prayer and Subh as a Sunnah prayer?

If the time for Fajr begins with the clear appearance of the true dawn (al-Fajr al-Sadiq), it is prescribed for the Muslim to pray two rak'ahs with the intention of the Fajr Sunnah (the desirable Fajr prayer or the two rak'ahs of Fajr). These are an emphasized Sunnah that the Prophet consistently observed. After that, one prays two rak'ahs, which are the obligatory Fajr prayer (also called Subh). Subh and Fajr are two names for the same entity, which are the two rak'ahs of the obligatory prayer.