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.
Ibanez reissued the narrow TS-808 as the "35th Anniversary TS-808" in 2014.
It is a very accurate reissue except they used JRC4558D chips instead of the 1458 chips.
SRV used the TS-808 for his trademark juicy strat tone.
When he used smaller Fender amps that had natural overdrive, he used the TS set clean (low drive setting) with the level up high to push the amp for more distortion (see my CLEAN BOOST info below).
The most popular use of a tube screamer is to push a tube amp to make it overdrive more, but they sound good through almost anything.
If you are a geek like we are, check out this awesome article Tube Screamers Secret for some cool info about why the tube screamer circuit sounds so good.
Externally the on/off switch grew to fill about 1/3 of the effect.They have a little bit more grit which some people might like.The early TS808 used a circuit board marked MP-D01201A, then in late 1980 or so they changed to the MP-D01201B board.The lighter green OD-855 Overdrive-II is also in the TS-808 style box and has a circuit which is similar to the 808 - the board part numbers only differ by one digit.The overdrive and OD-II had a different, much more distorted, fuzzy circuit close to a Big Muff.We have a mod to make these the same as the originals.Early TS-808's have the Ibanez (R) "trademark" logo which some people seek.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".This is also Jim Weider's favorite chip in the King Of Tone pedal.Some of the early TS-808s also have a nut holding the power adaptor jack on, while later ones have no nut and a flush adaptor jack. You can see one of the Narrow Euro TS-808 pedals, it's the leftmost of the TS-808s. The bottom right is the original orange Ibanez Overdrive, with the slightly later OVERDRIVE-II on it's left, with the last version OVERDRIVE-II one more to the left.