Hello Greg, welcome to the forum.
There are two basic types of coal stoves: hand feed and stoker feed.
Hand feed is like a wood stove, you have to add the fuel directly into the firebox and the fire. With coal this is usually done with a shovel or a bucket.
Stoker fed stoves have a hopper to hold a day up to several days worth of coal, this is fed to the fire by a mechanism, [there are several types] and the ashes end up in the ash pan.
As coal burns, the coal is reduced to ash. This ash tends to block the air getting to the coal, so in stokers, the ash is pushed ahead of the fresh coal, and the fresh coal has access to oxygen.
In hand fed coal fires, the ash will end up smothering the coal, and reducing the heat output of the fire. These units have a grate in the bottom of the firebox that has moveable sections, and there is a handle on the outside of the stove allowing the owner to shake the grate. The shaking gets the ash to fall through the gaps/holes in the grates and into the ashpan. This shaking is usually done twice a day, as part of the loading of fresh coal to the fire.
There is a thread here on the forum showing what some stoker mechanisms look like: http://nepacrossroads.com/viewtopic.php ... +mechanism
There are lots of photos of hand fed fireboxes as well. Going to manufacturer websites often will show firebox designs in line drawings.
Corn and pellet stoves are stoker type stoves, wood stoves are hand feed.
Hope this helps. Greg L