Dolby Digital is a catchall term which includes Dolby Digital, Dolby Digital EX, Dolby Digital Live, Dolby Digital Surround EX, Dolby Digital Plus, and Dolby TrueHD.
Dolby Digital (AC-3) and Dolby Digital TrueHD (THD) is more common in cinemas, and far more common in homes.
DTS also has several variants- DTS, DTS++, DTS-HD, DTS-HD Master Audio
DTS-HD Master offers higher data rates than Dolby Digital TrueHD, and this has led to unfounded claims that DTS is better than Dolby Digital in sound quality.
However, under identical mastering conditions, the two systems are indistinguishable from one another, both being lossless formats, are bit perfect when properly decoded into Lossless PCM raw audio, producing exactly identical audio.