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.
These have a bottom plate that unscrews to change the battery like an MXR pedal, no plastic battery cover. It uses two 1458 chips which are the 1st version of the low-tech dual op-amp.
As you can see, the JRC chip was used throughout the life of the TS-808 and the TL4558P was used sometimes.
In AB tests, there is VERY little difference between the three chips, although the JRC gives the strongest CLASSIC tube screamer sound- the sweet vocal midrange.
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).