The TS-808 and its generation have small square metal on/off touch-buttons. There were some TS-808s made in the 1979 period, mostly for other than USA markets, that came in a narrower box.
The main change in the TS-9 circuit is in the output section.
This caused the tube screamer to be a bit brighter and less "smooth".
There is really no difference, although some of these have a Malaysian Texas Instruments RC4558P chip instead of the normal Japanese JRC4558 chip.
A rare chip used was the TL4558P chip, as used in some early 8-pin IC chip Boss OD-1 pedals.
The Edge from U2 uses a TS9 for most of his overdrive tones, as do countless other famous rock and blues players.