Radio Broadcast Data System is the official name used for the U.S. version of RDS, though the "RDS" name seems to be at least as common in daily usage. The two standards are nearly identical, with only slight differences, mainly in which numbers are assigned to each of the 31 music and other program formats the RBDS system can identify.
Generally, mobile phone RDS implementations make use only of Radio Text info. It's 64-character free-form textual information that can be either static (e.g. station slogans) or in sync with the programming such as the title and artist of the currently-playing song.
Mobile phone FM tuners don't receive some of the RDS information that may be available, such as time, program type (PTY) or traffic announcements (TA/TP).