Impossible to describe... you have to actually hear them.
but..
The ts-808 evolved from the original 70's Ibanez Overdrive with the orange casing. It's used by SRV etc... and produces a very natural sounding and smooth overdrive supposedly recreating the tone of tube distortion.
The 808 was succeeded by the TS-9 in the early 80's. No clue what the TS-9dx is unless that's the recent re-issue.