The open claw style map is where the sphere is cut at the back with a cross shaped cut (as you'll see in the V4 sclera uv) to unfold, producing a vaguely X shaped map. Sphere style is usually produced when a hemisphere style geometry is mapped with a planar normal style mapping, as seen on the V4 eyesurface uv. I've found that the claw style mapping is better at reducing distortions toward the back of the uv area and has a better range of distortion free horizontal image area for texturing. The sphere style is used often when visible area of the uv is of lesser importance. Self explanatory considering the above why V4's eye uv's were mapped the way they were, although I think that whoever did the mapping perhaps went overboard in fiddling with the maps in terms of end user friendliness (perhaps so with the geometry also).