As in chess, it helps to be able to see your next move in advance. If you encounter a situation of distress, it is not necessarily an emergency if you have a plan of action to address it. For example: You fall out of your boat, but it is not necessarily an emergency if you can re-enter. In fact, experience will help an individual develop an entire chain of contingency plans. Big wave = brace-> roll-> wet exit -> reentry and roll -> paddle float -> etc. Between each stage of that chain, you have your OODA loops (observe, orient, decide, act) running and telling you what to do next, so the sequence will vary depending on the individual and their experiences. Obviously, different people will have different chains of different lengths: Beginners will have shorter chains that run slower, and experienced peoples will have longer chains that run faster. Subsequently, an emergency occurs at different points for different people.
For a newbie, capsizing alone in the ocean may be an instant emergency situation. They have virtually no reaction chain to move down, and they find themselves instantly in mortal peril. Because they don’t have the skills or knowledge to make a proper decision and act on it, they are effectively stuck on notch one of their chain. If they are cool headed, they will able to observe and orient themselves. If they are lucky, they will be able to make a good decision with which to act on, and get him/herself back on board. Maybe. The alternative is that they panic or make a poor decision, and subsequently find themselves more fodder in Davy Jones’ locker.
For an experienced paddler, capsizing alone in the ocean presents very little risk without compounded hazards. Since they have a long chain of reactions to draw from, they know exactly what to do when they capsize. In fact, given enough experience, they have probably predicted what is about to happen (i.e. capsize) and are already setting up for their first roll attempt. Because the experienced paddler has developed his skills and knowledge, he has more relevant and preprogrammed knowledge to run through his OODA loop. He reacts quicker and more appropriately.
Of course, no one is immune to an emergency. Take the same experienced paddler and give him a heart attack on a paddle 3 miles off shore. Or take something like X15’s example: Surf yakker blows three roll attempts, has to wet exit, and is now about to be pounded on a cliff, reef, rock, whatever.
Emergencies happen when one has no wherewithal to address their distress. They can happen anywhere, any time, and to anyone. You can arm yourself with knowledge that puts emergencies more at bay, but you cannot immunize yourself against them entirely. The single most important piece of knowledge you need to deal with an emergency is learning how to acknowledge an emergency. You need to learn how to say to yourself “I do not know what to do, I am in danger, I need help.”
For me, I consider a situation an emergency when I hear that phrase in my head, “I don’t know what to do.” I consider another in an emergency when I can look at them and say “They don’t know what to do, they need help.”