Yes the 808 is smoother and more compressed than the TS-9. The TS-10 sits somewhere in between the two. It's very subtle though especially used as a boost.
But generally speaking, from smoother to brighter: 808, TS-10,TS-9, TS-7.
TS9 vs 808
Re: TS9 vs 808
There is very little difference except for the op amp which varied over the years.

If you are comparing 2 or more pedals, the difference is more likely parts tolerance.
History
https://www.analogman.com/tshist.htm

If you are comparing 2 or more pedals, the difference is more likely parts tolerance.
History
https://www.analogman.com/tshist.htm