Basic ADS is part of FANS, whereby the aircraft will send position reports (when requested) when logged on to ATC.
However, ADS-B is something different and refers to a GPS position squitter which is transmitted irrespective of whether you are operating in the FANS environment. ADS-B is transmitted by Mode S (if capable) and can be received by ATC Ground Stations or other aircraft capable of receiving ADS-B. New generation TCAS systems can track and display ADS-B traffic (called passive surveillance). ADS-B traffic can typically be tracked at greater ranges than normal TCAS traffic which is tracked via active interrogation.