Long Gun General refers to any firearm in Canada with a barrel longer than 18 inches, there are some rifles called carbines, that fall below this length thus still a rifle but restricted under Canadian law.
Hand Gun Generally a firearm that can be held and fired with one hand, generally short barrelled up 7".  There are some examples with12" though unusual.
Shot Gun

 

Generally a smoothbore gun that fires shot (lead or steal balls of various sizes, i.e. #7, #4) over short ranges. Also called scattergun. Sized in gages, 10,12, 16,20,410 etc.  (Can be rifled for shooting slugs)
Assault Rifle

M16A2 -(C) Armalite   AK47

'assault rifle' used to describe a military rifle that allowed the operator to choose semi-automatic or fully automatic firing of ammunition.  Original assault weapon, multiple shots with one loading, was the 1860 Henry as shown under lever action.

The press and Gun Control have changed this now to refer to  'Assault Weapons' a select group of semi-automatic rifles possessing certain features that made them look menacing i.e. Military. Fully automatic weapons have been banned from civilian use in most countries.

Can be Prohibited, Restricted or Non-Restricted dependent on type, manufacture, model designation i.e. AK anything, prohibited.

Bolt Action Rifle

Lee Enfield No4.

Bolt Action rifle most frequently used on rifles, some specialist handguns,  whereby a cylindrical shaft, controlled by an attached lever, manually feeds a cartridge into the chamber, turns down engaging locking lugs in recesses in the front receiver ring, allows firing by the fall of an internal spring-loaded pin, on opening this starts extracting, recocking and ejection of empty cartridge, preparing for the next shot.

Non-Restricted Long Gun

Double Action Revolver

Double action revolver an action type, mainly on revolvers, where pulling the trigger through a long stroke revolves the cylinder, cocks the hammer and fires the gun---and alternatively, where manually cocking the hammer and then pulling the resulting single-stage trigger fires it also.

Restricted firearm in Canada, barrel less than 105mm Prohibited

Full Automatic

A full automatic firearm that reloads itself and keeps firing until the trigger is released

Prohibited (Illegal in Canada, and most countries)

Lever Action Rifle

Henry Rifles (Uberti)

In a Lever Action rounds are loaded via the movement of a lever type action, downward with the hand, that cycle the bullet.  The Winchester Lever action is the most famous of these.

Non-Restricted Long Gun

Pistol

Pistol original referring to a semi-automatic handgun.  Used to-day to refer to any handgun, by media.  To day can be termed single action or double action, this is determined if the first pull of trigger cocks the hammer (Double action) or not, Single action.

Restricted firearm in Canada, barrel less than 105mm Prohibited

Pump Action

A pump action firearm that loads when a manual device as pulled back buy the hand, thus opening the action, ejecting a spent cartridge, and picking up a new one.  Mainly used in shotguns, some pump rifles have been made.

Non-Restricted Long Gun

Semiautomatic Rifle

A semiautomatic firearm that reloads itself and each pull of the trigger.

Can be Prohibited, Restricted or Non-Restricted dependent on type, manufacture, model designation i.e. AK anything, prohibited.

Single Action Revolver

Colt SAA Single Action

Single action revolver an action type, manually cocking the hammer and then pulling the  single-stage trigger fires.  The backwards movement of the hammer revolves the cylinder, cocks the hammer.

Restricted firearm in Canada, barrel less than 105mm Prohibited

Single Shot Rifle

Springfield Trapdoor 45-70

Single shot this type of firearm, can only be fired one shot at a time before manually reloading, i.e. mussel loaders, trapdoor, rolling block and many specialist competition rifles and handguns.

Non-Restricted Long Gun, Restricted if handgun.

Black Powder Black powder firearm generally refers to a firearm that is a replica or original firearm built for the original Gun Powder, thus Black Powder.  There are modern day muzzle loaders that are designed for black powder.  Modern powder is generally referred to as smokeless, and is dangerous in old guns.