What, if any, are the differences between hemiwicking and wicking?
I'm not especially familiar with the detailed differences between the two much beyond the definitions you've posted here, but it seems to me that:


Wicking occurs in the bulk volume of a porous substrate, not just on the surface; whereas
Hemiwicking occurs strictly on the surface of an otherwise impermeable substrate


As you note, in both cases the fluid movement is driven by capillarity, however.


  My assumption would be that Wenzel wetting would actually be an example of wicking?


I disagree. All three panels of the figure you've posted look to me as though they are trying to illustrate strictly surface phenomena, and thus none of them are forms of wicking.  The main difference between (a) and (c) is that in (a) the structured surface is wetted only immediately adjacent to the liquid drop, whereas in (c) the surface is wetted in an area beyond the extent of the drop. Thus, the Wenzel wetting is neither wicking nor hemiwicking.