From what I know, the 5100mAh version is the newer version that supports fast in and fast out (supposedly charge powerbank fast, powerbank charge phone also fast). It came out together/after the S7 series i think. Don't remember seeing this before the S7 came out.
See this link from Samsung.
http://www.samsung.com/nz/consumer/mobile-devices/accessories/battery/EB-PG930BBEGWW
the 5200mAh thin version is the older version that came out with the Note 5 i think. When using the Note 5 already saw the thinner version around in stores. That one from info i can find only support fast out, not fast in.
Edit: The 5100mAh and 10200mAh came out together at the same time. The size is very different for both. (
http://www.androidheadlines.com/201...ts-fast-charge-battery-pack-in-new-video.html) Sorry for the AH link, but it's the first article i found with a picture.