First of all your question seems to be about appendages. In principle appendages keep a boat from making leeway. They come in many shapes and sizes. Keels are supposed to be a fixed appendage and centerboards generically are moveable appendages that occur on the centerline but centerboards are just one kind of moveable appendage. In more detail:
The earliest form of a keel was simply the backbone of the boat extending through the bottom planking. (Like a Viking ship) That works OK with running and reaching sails but when you try to point toward the wind you slip side wards at great speed. As sails and rigs
were invented that allowed boats to point toward the wind the keel was extended below the boat either by planking the hull down to a deeper backbone or by adding dead wood (solid timber below the backbone. A planked down keel permitted the space between the planking to be filled with heavy material (originally stone) which served as ballast keeping the boat from heeling. After a while it was discovered that there were advantages to bolting a high density cast metal ballast to the outside of the deadwood and interior ballast dropped out of fashion.
These earliest keels pretty much ran from the point of entry at the bow, to the aft most point of exit at the stern. Those are full keeps in the fullest sense of the word.
They have some advantages; they theoretically form a long straight plane which keeps a boat on course better (greater directional or longitudinal stability). If you run aground they spread out the load over a larger area reducing the likelihood of damage. Once really planted they keep the boat from tipping over fore and aft. They are easier to haul and work on. You can spread out the ballast over a longer distance and so they can be shallower. You have a greater length to bolt on ballast so it is a theoretically sturdier and simpler connection.
They have some disadvantages; they operate near the surface and near the intersection of the hull and keel which are both turbulent zones. They also have comparatively small leading edges, and the leading edge is the primary generator of lift preventing sideslip. Because of that they need a lot more surface area to generate the same lift. Surface area equates to drag so they need more sail area to achieve the same speed. As a boat makes leeway water slips off of the high-pressure side of the keel to the low-pressure side of the keel and creates a turbulent swirl know as a tip vortex. This is drawn behind the boat creating drag in a number of ways. The longer the keel, the bigger the vortex, the greater the drag. So they need more sail area again to overcome this drag. To stand up to this greater sail area the boat needs more ballast and a stronger structure, which is why long keelboats are often heavier, as well. (Of course more sail area is needed to overcome that weight as well- once again weight adding weight) They tend to be less maneuverable.
In my book, based on the traditional definitions that I grew up with, any keel that is less than 50% of the length of the boat on the bottom of the keel is a fin keel. Fin keels came into being in an effort to reduce drag. Cut away the forefoot or rake the stem, as well as, move the rudderpost forward and rake it aft and pretty soon you have a fin keel.
Today we assume that fin keels means a keel with a separated rudder (skeg hung or spade) but in fact early fin keels had the rudder attached (in a worst of all worlds situation)
Fin keels with separate rudders seem to be the most commonly produced keel form in the US these days. (I could be wrong, there is a resurgence of full keels these days)
Fin keels have some advantages as well. They have less drag as explained above so they typically make less leeway and go faster. You can get the ballast down lower so in theory they are more stable for their weight. They are more maneuverable. They take better advantage of the high efficiency of modern sail plans and materials.
They have some disadvantages as well, many of these have been offset or worked around by modern technology but at some level they are still accurate critiques. They have less directional stability than long keel boats so the tend to wander more under sail. Since directional stability is also a product of the dynamic balance between the sail plan and underbody, in practice they may actually hold a course as well as a full keel. In general though you can expect to make more course adjustments with a fin keel. It is sometimes argued that it takes less energy to make these corrections so a fin keel may also require less energy to maintain course. This I think is a product of the individual boat and could lead to a debate harder to prove than the number of angels that can dance on the head of a pin.
Fin keels are harder to engineer to withstand a hard grounding and when aground they are more likely to flop over on their bow or stern. (Although in 39 years of sailing, I have never heard of anyone actually experiencing this.) Fins typically have deeper draft. They are easier to pivot around and get off on a simple grounding.
A shoal keel is just a keel that is not as deep as a deep keel. Today the term seems to be applied mostly to shallow fin keels. Shallow full keels seem to be referred to as shoal draft boats. (You guys notice that as well) A shallow fin is a tough animal to classify. I really think it has few of the advantages of either a deep fin or a full keel and has many of the worst traits of both full and fin. This can be partially offset by combining a shallow fin with a centerboard, which is a neat set up for shoal draft cruising.
A lot can be done to improve a shallow fin. One way is to add a bulb. A bulb is a cast metal ballast attachment added to the bottom of the keel. They concentrate the ballast lower providing greater stability and sail carrying ability than a simple shallow keel. Traditionally bulbs were torpedo or teardrop shaped. They have been re-contoured to provide some hydrodynamic properties. Remember tip vortex from above. Shallow keels need to be longer horizontally than a deeper fin in order to get enough area to prevent leeway. This means that it would generate more tip vortex and more drag than a deeper keel. The bulb creates a surface to turn the water aft and prevent it from slipping over the tip of the keel thereby reducing tip vortex. This does not come free since a bulb increases frontal area and surface area.
Wing keels are a specialized type of bulb keel. Instead of a torpedo shaped bulb there are small lead wings more or less perpendicular to the keel. These concentrate weight lower like a bulb and properly designed they also are very efficient in reducing tip vortex. There has been some discussion that wings increase the effective span of the keel when heeled over but this does not seem to be born out in tank testing of the short wings currently being used in production sail boats. Not all wings are created equal. They potentially offer a lot of advantages, but they are heavily dependent on the quality of the design and I really think that many wing designs are not really working to their potential.
Keels that are not really keels:
Swing keels are ballasted centerboards and drop keels are ballasted daggerboards that are ballasted beyond what it takes to submerge themselves. They are really forms of centerboards. More on them in with centerboards.
Keels that are keels that move.
I said that keels do not move. That used to be true. We now have canting keels, which can be pivoted from side to side. They are best designed to be light fins with heavy bulbs that can be canted to windward increasing the effectiveness of the righting aspects of the keel. Just one problem, a keel canted to windward losses efficiency to prevent leeway so they really need other foils to keep leeway in check. I frankly do not like the idea of a canting keel. I think canting keels are too complex and potentially problematic.
Centerboards are appendages that can be raised and lowered on or near the centerline of the boat. They can rotate up into a trunk or rotate below the boat. Daggerboards are a type of centerboard that raises vertically or near vertically in a trunk. Swing keels are a type of rotating centerboard that actually contains a substantial portion of the boat''s ballast. They may be housed in a trunk like a Tartan 27 or 34 or hung below the boat like a Catalina 22. In the case of the Tartan 27 or 34 they are more frequently referred to as a Keel/ Centerboard (abbreviated k/cb) A swing keel is intended to act as a fin keel when lowered and allow some sailing in the partially raised position. My biggest problem with swing keels is that most do not have a positive lock down. In an extreme knockdown they can slam up into the hull greatly reducing the boat''s stability and can damage the hull. This is actually a pretty rare occurance and usually requires big wave action combined with a lot of wind, but I personally have experienced that phenomina while sailing out in the Atlantic. They tend not to sail as well as a fin keel but if you play the drop keel, down on a beat and up on a run, they can do reasonably well.
A drop keel is a daggerboard that actually contains a substantial portion of the boat''s ballast. These are easier to lock down but can be more easily damaged in a grounding. They generally have better shape than a swing keel and can be more robust, but not always are. They can have a bulb and be almost as efficient as a fin keel.
Other appendages: (besides the rudders)
Bilge keels (for our English friends) are a pair of keels (usually fins these days) that emerge on either side of the boat and angle out. They offer some advantages. If you let the boat dry out the boat can stand on the two keels and wait the next tide. There are dubious theories about increased efficiency since one is vertical like a good leeway resisting foil and one is canted like a good stability inducing foil. They do allow shallow draft though but boy are they a pain to free once aground.
Bilge boards (for the scow guys), are a pair of centerboards that angle out of each side of the boat. They work well on scows but I''ve never been able to really figure out scows anyway. Seriously, You raise the windward board and lower the Leeward one on each tack and because they are close to vertical they can be small and efficient. I still don''t get the scow thing.
Last but not least- Lee boards. Leeboards are foils that are bolted to the side of the hull like on Dutch Jachts and Herreshoff Meadowlarks. Phil Bolger''s sharpies use them a lot as well. They have some advantages but they drive me nuts. They are vulnerable in docking and ideally are raised and lowered on each tack also. Some are raised to be hinged feather so they do not need to be raised.
So that''s about it. The final is tomorrow- multiple choice and essay.