What is the difference between Fajr prayer and Subh prayer, and what does a Muslim do, in emulation of the Prophet, peace and blessings be upon him, from the first call to Fajr prayer until the second call or after it in congregational prayer?

The dawn (Subh) and pre-dawn (Fajr) prayers are two names for one prayer. The two rak'ahs of Fajr are the supererogatory sunnah prayer performed before it. This is among the most emphasized sunnah prayers. It is sunnah to make them light and to lie down briefly on one's right side afterward. It is also sunnah to go to the mosque early and to be keen on the first row and the opening takbeer (Takbeerat Al-Ihram). It is also from the Sunnah to sit in the prayer area after the Fajr prayer, reciting remembrances (adhkar) and remembering Allah until the sun rises, and then to pray the two rak'ahs of Ishraq.