Essentially the ADS-B transmissions are used by the TCAS collision avoidance systems on the aircraft, and Mode S generally is used as an upgrade to Mode C altitude-encoding transponders.
The ATC radars obtain a skin paint by the normal process of reflecting pulses from an aircraft and detecting their return, but that is a very blunt instrument and provides no real information on the target thus seen. So Secondary Surveillance Radar is used, which is a bit of a misnomer, because it isn't radar it is a transponder system. The interrogator operates at 1030MHz and the aircraft then transmits back at 1090MHz, the S in Mode S means 'select' which is a selective interrogation method whereas with Mode C all aircraft in range would respond to incoming 1030MHz signals and in dense environments that leads to many signal collisions.
I'm sure some Googling will lead to more information on the subject.