Looking at the Stole_(clothing) wiki, the very provided examples are clearly different.
post #905361
This form of stole covers a portion of the chest from left to right--no gaps left behind.
post #6133616
Not on the wiki, but very similar to the above--and a reasonable take on it. Characters with long hair may have an easier time fastening it around the neck rather than sliding it over their head.
post #760201
This form is a boa_(clothing). Sometimes not even worn around the neck, just the arms.
post #20254
Also not a part of the wiki page, but this is a piece of fabric worn between the arms, similar to boas, also tagged as a stole.
post #2957362
This is a clergy scarf, commonly worn by religious figures.
I happen to like the first two forms of stole and want to more easily locate images like that, but as it is they're kind of just shoved into the same term. Even trying to search outside E621 it's impossible, so I suppose there's no real terms for them, but perhaps something like full_stole for the first two, and clergy_stole for the religious vestment? Something similar for the arm fabric and boas, if those should fall under the term too, and then the existing stole_(clothing) tag could be an umbrella term?