So what are convex edge shears and how do they differ from single-bevel? Household and kitchen scissors are single- bevel - they have one angular cutting surface on each side of the scissor that cuts when the two surfaces come together - see picture below - the shiny part is the single-bevel.
The back of a convex edge is shaped like half of a parenthesis - a continuous curve end-to-end. See first picture below. The flat hone machine is engineered to maintain that curve as it hones. A skilled sharpener uses a flat hone to remove just enough metal to remove imperfections from the convex edge.
The opposite side of that convex edge is the cutting edge or "ride line." Japanese water stones create the (shiny) ride line you see in the second picture. Convex shears cut hair where the two ride lines meet.
