The M781 is the "direct mount capable" version. This means the bracket axle assembly (the small plate between the main pivot point and the RD hanger - sometimes also called a 'B2' assembly) can be removed, and the the main pivot point screwed directly into a swept back RD hanger.
It's a modification Shimano have quietly introduced for all their 2013 mechs, but which has received a less than enthusiastic reception by the industry, with only a few of the more niche bike builders using this capability. You might find it more widely adopted in the future though as more bolt thru rear axles appear on bikes.
If your bike has a 'normal' RD hanger then it essentially makes no difference whether you get an M780 or M781. The M781 will work in both modes, so you're a bit more future proofed, that's all.
If you want to see what one looks like in "direct mount" mode, then click here
Rotwild 2013 - 650B Enduro und weitere Neuheiten von der ISPO Bike and page down to photo no. 9. Notice the swept back RD hanger, and the absence of that extra little plate between the RD hanger and the main pivot point of the RD (and yes I know thats a shadow+ RD, but it was the only picture I could find of a direct mounted RD, and the principle is the same).