I'd always understood that the JT2 S was primarily intended as as male taper for drilling machines. Presumably exploiting the shorter body and shorter taper in the design of the machine to gave a greater distance between drill and table for the given overall size.
The slightly smaller diameter allows a 14 mm Ø spindle to be used whilst the full size version needs either 9/16" or 15 mm Ø.
Overall it seems an awful faff to save 1/8" in length. But sizing of Jacobs, like Morse, tapers is somewhat less than logical.
However according to Yukiwa Seiko, a Japanese maker of drill chucks and other tooling, **LINK** :-
JT2S is a short type of Jacobs taper No.2. The taper angle is the same as JT2, but the taper length is a little shorter than JT2. As the difference is just the taper length only, it is possible to mount a JT2S drill chuck on a JT2 arbor. Generally, JT2S taper is usually used in Japan while JT2 is popular in U.S.
So the preference may be largely geographical these days.
Clive