There is a difference between surface edges and isocurves.
Edges are intrinsic parts of a surface object in the sense that they explicitly define its borders. Surfaces can have “naked” (open) edges, “manifold” edges (joined to one other surface), or “seam” edges (joined to itself as in a cylinder) in any combination.
Isocurves are more or less artificial in the sense that they represent the NURBS curve that defines the surface in one direction at some arbitrary point along the surface. There are an infinite number of possible isocurves in either direction. By default, with isocurve density set to 1, Rhino shows you the “middle” isocurve of a surface. There are however a few “special cases” such as a cylinder or a sphere - you get 3 plus the seam, in order to better show the object in wireframe. You can turn off isocurves if you like or increase their density.
Isocurves do not however represent visible tangent edges of something like a cylinder as you might expect. Tangent edges that do not coincide with visible seams or isocurves are not shown at all in Rhino wireframe display modes.
Note also that Rhino 5 has a new type of object, called an extrusion object. The creation of extrusion objects is on by default in Rhino 5 and a number of the familiar primitives that were polysurfaces in Rhino 4 are extrusions in Rhino 5, including boxes and cylinders. Extrusion objects may have different isocurves than their polysurface equivalents, and they have none at all in the extrusion direction.
Below is a sphere and a cylinder surface in wireframe with isocurves set to 1 versus turned off. Note the sphere is no longer represented by anything but an arc (the seam edge) when isocurves are off.
I hope some of this explains what you’re seeing here…