Gouge

A gouge is a chisel-like edge tool ground with a curved (concave, on the cutting face) blade rather than a flat one, letting it cut a hollow or a curved profile a flat chisel can't follow cleanly. Carving gouges come in a wide range of "sweeps" (how deeply curved the blade is) matched to different carving needs, from nearly flat to nearly a full half-circle; turning gouges, used on a lathe rather than pushed by hand, are a related but distinctly shaped and handled family of their own.

A skew chisel, despite the name, is closer kin to a turning gouge in use than to a bench chisel -- ground with its cutting edge angled rather than square across the blade, it's a lathe tool used for planing cuts and V-cuts on spindle work, prized for leaving an exceptionally clean surface straight off the tool with no sanding needed.