Most grooming scissors have a beveled or German edge. Beveled scissors are sharpened, honed, cleaned, lubricated and adjusted.
Convex edge scissors have become more common in the grooming industry over the last several years. They need to be very sharp, and are great for finish work, but the edge will not hold up well if you use them to rough out a dirty dog. Blade Runners will disassemble, sharpen, and hand hone your convex shears.