To the OP..great job! I've done several of those starters. They are always fun.
The mystery wire that the OP's starter has and the second starter did not is a shunt. I'm not totally versed in electric motors either, but essentially, the shunt serves as an rpm limiter so that the starter motor does not overspeed, especially once the engine catches bit before the key is released. It diverts voltage once the starter motor spins up to a certain point. Someone will probably jump in and correct me after this being posted a year and a half but that's as well as I can explain it.
The reason the OP's starter has it and the other doesn't and never did is that the OP has the first gear reduction starter model...2095150, which is a 3-series, 1-shunt starter used from 1962-69, as was the 2875560 starter used from the very tail end of 1969 production until the end of 1972 production. Somewhere around that time engines started getting "smogged", detuned and harder to start, so Chrysler deleted the shunt coil and turned the starters into straight 4-series(4 coils) starters to speed them up. Shortly thereafter, the coils were enlarged to speed the starters up yet again. That's why the early starters turn slower but don't have that awful, grinding wind-down sound the later versions do, especially the reman units.
Around 1974 Chrysler also introduced the "large frame" starter which has a larger field housing and different gear ratio, to be used on big-blocks and eventually everything. Those have their own unique sound. Also, there WAS an early starter that had no shunt...part #2098500. Used on 1963-ONLY 225 slant six and all 170 Slant six engines. I have one and it does indeed spin faster than the 2095150. To this day I have never seen an explanation for why that starter existed.
Hopes this helps. BTW, did you remember to install the leather brake washer between the large driven gear and the gear housing? They exist. I had to order mine from some obscure outfit. They tend to wear away pretty fast..I have only encountered one used starter that still had one.