Finishing (chisel) = Heavy Duty (in Hans Karlsson speak) = Registered (Mortice chisel) = Roughing = "Double Hoop Striking Gouges" (HK/Country Workshop) = Butt (chisel)
= A heavy duty chisel designed to be hit with a mallet. Usually it has a brass ring around the end of the handle to protect the (usually wooden) handle and prevent it splitting.
The stem of the chisel/gouge may be thicker than "normal" (i.e. thicker than a "paring gouge" - see below). "Finishing" is a mis-spelling of the original French word for such tools.
Paring (gouge)
A regular gouge, that does not have the heavy duty features described above. The name comes from French and refers to peeling, as in peeling an apple.
The tool is not intended to be struck by a mallet, rather it is pushed by force of hand and, possibly, body weight.
"Out cannel"
A gouge with the bevel on the outside. Used generally, and favoured for bowl carving, this gives the tool a tendency to lift out towards the end of the stroke, rather than a tendency to bury itself ever deeper, allowing gradual tapered shavings to cut. The more general purpose option(?)
"In cannel"
A gouge with the bevel on the inside. More limited in scope. Better for gouging in a straight line(?) and on external surfaces. [Haven't come any big proponents for this grind option.]
Motrice (chisel)
A deep, narrow chisel, designed to cut out deep, narrow, rectangular holes ("mortices") that provide the female end of a mortice and tenon joint.
Pig-sticker (mortice chisel)
A traditional English design of mortice chisel, which has a characteristically (dagger-like) long blade, rather than a shorter, stubbier one.
Spoon gouge
A gouge that is shaped like a spoon, rather than a gouge designed to make spoons (in fact Drew Langsner writes that they are not suitable for spoon/ladle carving).
Except for Hans Karlsson spoon gouges, which are designed for carving out spoon bowls.

"Dog-leg" Gouge / Trog Runner
A gouge with a stem that is doubly bent, like a dog's rear leg. Used to gouge in difficult to reach areas, such as the bottom of a steep-side bowl/kuksa.