The difference between medium crown and narrow crown staplers are based on the applications in which they are used. As the name implies, the narrow crown stapler fires a narrower staple (approx 1/4" wide) and is used for more of a finish application (i.e. stapling backs onto cabinets). Also, the wire gauge is thinner (18 gauge) to prevent splitting the wood in the finish applications.
As for the medium crown stapler, it is used for more rough construction applications where more holding power is required from the staple. The staple is wider (either 7/16" or 1/2") than the narrow crown and the wire gauge is thicker (16 gauge). The medium crown staplers/staples are used to apply floor sheathing and roof sheathing as well as OSB/plywood sheathing on the walls of a newly framed home.