Jeppesen defines the ADS-B as a surveillance system broadcasting GPS-derived positions and other information such as velocity over the data link. Yet, the Wiki article on ADS-B relates it to the Mode S transponder system. So the ADS-B operates either on a GPS or on Mode S. Is my understanding correct?
ADS-B, Automatic Dependent Surveillance - Broadcast, is a broadcast of the aircraft's position and other information.
The position is determined by a GPS receiver. It is possible to use another qualified position source, but today it is de facto GPS. Other GNSS (Galileo, GLONASS, Bei-Dou) are other likely candidates in the future, but as far as I know, none have been certified for ADS-B yet.
The broadcast is usually by the Mode S transponder but can also be done by a dedicated transmitter / transceiver in the Mode S format and frequency (1090 MHz).
In the USA below 18 000 ft, in addition to the Mode S based ADS-B, a system based on Universal Access Transceiver (UAT) is used. This operates on 978 MHz
A third broadcast system was VDL mode 4, it was never rolled out on large scale.
So ADS-B uses GPS to determine the position and it operates either on 1090 MHz (a frequency also used by Mode S) or 978 MHz to broadcast information.