I'm a little confused.

A razor has to be sharp or it won't cut. My test for this is the against the grain cut. If the blade is not sharp, it will snag and stop.

A smooth razor slides comfortably over the skin.

Sharp is to do with the edge and smooth is to do with the bevels.

In my experience the Escher or Escher type hones (not Thuringiens) have a finer grit than the coticule and produce the sharper edge and smoother edge.

It's interesting we all have different experiences and for me it just tells me that no two natural hones are alike.