are the Mode S transponders used for the ADS-B transmitions also or are those seperate transponders entirely
The short answer is yes, ADS-B is transmitted from the Mode S tranponder.
There are three radio technologies that are in use for ADS-B. The one that is most common is working on 1090MHz, the same frequency as SSR.
If an aircraft has a Mode S transponder, the ADS-B transmissions will be send from this transponder. The 1090MHz ADS-B has the same pulse format as the Mode S replies. It is this technology that is used all of the international ADS-B developments.
The two other ADS-B radio technoligies are UAT (Universal Access Transceiver, 978 MHz) and VHF Data Link Mode 4.
UAT is used in the USA for smaller aviation, up to an altitude of 18000ft. This ADS-B transceiver can be used together with a Mode A/C transponder, or ATCRB as they prefer to call it over there.
VDL Mode 4 never really took off; there are still a few aircraft that have it in Sweden and Russia perhaps.