DTS had (as in the past) a lossy compression scheme that allowed for 1.5 Mbps of the DVD's mux rate to be allocated to audio. That often wasn't used because there still had to be a DD (or PCM, but that'd be stupid) track, as DTS was an optional part of the spec. 1.5 Mbps plus at least 256k for the backup DD (and each additional language) was too much for most to give up. But the 1.5 Mbps DTS was the best sounding audio available on DVD.
In order to be more accepted DTS made a 768 kbps variant of their codec. While it still sounded good, it was obvious why DTS sounded better than DD with it's 384 kbps rate. Their algorithm just wasn't as good at compressing, but still benefited much from the larger bandwidth allocation.
When it comes to the modern TrueHD vs HD Master Audio, there is no difference. They are both lossless. Studio's seem to prefer DTS's offering, maybe because their name still makes people think they are getting more.
PLII can't be applied to 5.1 sources. But PLIIx can be used to turn 5.1 to 7.1. When I have PLIIx set, and feed my receiver 7.1 audio, it also turns off, just as PLII would turn off for a 5.1 feed.
