When you go to buy a sea kayak, and to a lesser degree a transitional kayak, one of the considerations you're going to have to face is what type or style you want. Traditionally, there were three types to choose from: Greenland, British, and North American. Lately the water has been muddied a bit with Current Design introducing Danish style boats, and with the new fast-touring style boats. Paddlers can be pretty passionate about the different types of boats, and there's a reason for that: it makes a big difference which type you choose. So what are the differences?
Greenland: This is where it all began, so these are the most traditional kayaks. They are typified by hard chines, a tight fit and small cockpit, and long slender shape. They are excellent for rolling, edge very well, and not surprisingly given where they come from, they are very capable boats in rough conditions. Beginning paddlers can find them twitchy but they reward persistence, and more experienced kayakers should give them a try. Maybe a skeg but never a rudder.
British: Tending to graceful lines, these look like a classic (modern) sea kayak. Fairly hard chines give good edging to create a playful style of boat, but one that is reliant on the paddler's handling. A skeg instead of a rudder, so steering is by edging and paddler strokes. Good for rolling. British boats are traditionally built with a heavier layup, reflecting the conditions around the UK. They range from longer expedition boats to shorter, more rockered surf boats.
North American: Stable, roomy "cruising" kayaks, always with a rudder. The addition of the rudder negates much of the need for edging, so North American style kayaks are multi-chined or soft chined, sometimes nearly rounded. This means they are stable and solid feeling, and with the rudder means the paddle is almost exclusively for propulsion (and less steering or stability). They're less good for rolling. Can range from broader versions emphasizing stability to narrower versions with an emphasis on speed and efficiency.
Danish: As the only manufacturer in this category, here's CD's description: "Stylish, snug-fitting hybrid of Greenland and North American hulls with Danish style". They are skeg boats, not ruddered, and the result of the design actually ends up being something like a British boat, but with a notably higher foredeck, enabling straighter knee position which in turn allows more effective torso rotation. Also range from tourers to shorter, rockered surf boats.
Fast tourers: Typically having a vertical bow leading into a deep V then a soft chine mid-section before V again to the stern. Always with a rudder, the emphasis is on speed and efficiency, so the paddle is kept just for propulsion. Uses range from fitness/ racing to day touring.