Having an unhealthy interest in 18th century warfare, sieges and fortifications, I can tell you (picked up from numerous sources over the years) that you should distinguish between:
- cannon - howitzer - mortar - pierrier
Cannon were meant to shoot in a straight line. They could be used as field artillery (when they were placed in between the troops in order to support them) in which case they were not too heavy and could be easily shifted using a couple of horse teams (we're talking 6, 8 and 12 pounders). These guns used up a lot of powder and until the appearance of shrapnel and other exploding projectiles were not very effective against infantry (they mostly relied on enfilading fire and they always tried to get off a good bouncing shot, thus magnifying the effect of a single cannonball by having it 'bouncing' through enemy lines and mowing the infantry down). These units could be horse artillery (light units to accompany cavalry units - means that they could gallop into action), horsedrawn artillery (heavier units - means that they could trot into position) and foot artillery, whereby the heaviest artillery pieces (e.g. the standard siege gun of the 18th century, the 24 pounder) was accompanied by its gunners and workmen (to prepare the position) on foot. The same type of gun was also to be found in fortresses, albeit on a heavier carriage.
Howitzers came into frequent use by the end of the 18th century. These guns had shorter and lighter barrels because they used a different technique of firing. While a cannon blasts away in a straight line, thus requiring a higher muzzle velocity, and, by consequence, a thicker and stronger (and heavier) barrel, howitzers lob their projectiles at their targets, needing a much lower muzzle velocity, using less powder and not requiring a heavy barrel. These howitzer used mainly exploding projectiles and were used as an infantry support weapon (often placed in between the 'carrés'

and firing at the enemy.
Now, do not think that cannons and howitzers fired at the enemy without seeing what they were firing at. Until the 1st WW it was standard practice to see what you fire at (I even have some pictures of a Belgian 75 mm battery firing at the Germans, while the Belgian officer in command is standing on a step ladder checking the effect of his fire). In the 18th and 19th century, cannons and howitzer only had a range of some 1500 to 2000 yds.
Mortars were heavy, short barreled guns, having no wheels (it was an American invention to mount mortars on railway platforms) and firing at an almost upright angle. They needed a sturdy platform in order to absorb the shock from firing the gun. These mortars normally used exploding bombs and were mostly used to bombard the enemy's fortifications or his advancing saps. This type of gun is very old and it was improved by a Dutch engineer Menno van Coehoorn, a contemporary of Vauban. This type of gun was still in use in some places by the end of the 19th century (some forts even had special batteries of mortars). The difference between a mortar and a howitzer is mainly that a mortar uses extreme high angles to fire and cannot be used for straight line fire, while a howitzer, if an appropriate charge is used, may be used for straight line fire (e.g. it is possible to use an M108 howitzer for ATK-fire, although it is not recommended to do so).
A pierrier was a type of mortar that was only used for firing loads of stone at the ennemy, in order to keep them away from guns or firing lines.
As to the change of name, I wouldn't really know whether there has been so much chnage of names. A mortar is nowadays a portable infantry weapon, using a light charge, thus requiring a light barrel. It can only fire at a high angle. Howitzers are the main infantry heavy support weapon, mostly firing at targets the gunners cannot see, while the only real cannon that are still about, are the tank guns.
Hope this doesn't mix things up too much.
Philippe Vanderghote