The short is for 1/2-inch walls, typically drywall; and the long has a 3/4-inch shoulder for plaster walls.
The two diameters cover different load ranges. The 1/4-inch can be used for up to 25 pounds and the 3/8-inch goes to approximately 50 pounds. I use the 1/4-inch for curtain rods, towel bars and large pictures. The 3/8-inch is good for handrail brackets and for existing oversized holes. These ratings are only estimates and vary with the strength of the wall and the type of use involved. An improper installation will provide no load rating.
To install, drill the proper hole, insert the molly and tighten the screw. At first, the screw will be hard to turn because the metal fingers have to start the bend. Then it will be easy to turn for the next dozen revolutions until it gets hard again. Now is when the anchor is clamping to the wall. Snug it up but do not kill it, especially when using a drill.
Occasionally the whole anchor will spin, digging a large hole in the wall. Stop, get a piece of metal you can hang on to with a small hole in it, and place it between the screw and the anchor. Keep the fiber washer against the screw head, as it is there to prevent friction when tightening. Now tighten the screw while holding your metal tool and the anchor will install easily without ruining the wall.