I find that people’s ways of reacting to fear stimuli fall into two general categories.
On the one hand, you have direct responses to the fear itself: attempting to in some way eliminate the immediate need to be afraid. For some people, this might be removing themselves from the location of the fear-source, or trying to find ways to banish it from their minds; it might be attacking someone who’s threatening them, or throwing increasingly desperate counters at the problem in hopes that one turns into a solution; halting as ideas race through their heads and are summarily discarded, trying to create a temporary barrier, beating around the bush until a better idea comes to mind—you get the idea. But what all responses have in common is that they’re trying to Do Something about the fact that there is something that causes fear and it is serving as a direct threat.
The coping mechanism, on the other hand, is another story. For some people, they’re there because the source of the fear cannot actually be combated; the only thing that can be done is to try to decrease its impact. Others have solutions they can implement, but the fear impedes them sufficiently that they need something to mitigate its effects while they put a solution into play—a stopgap, if you will. That’s where coping mechanisms come in: they’re there not to solve the problem of the fear, but to decrease it enough that the user can still function well enough to do what needs to be done.
So how do they stack up when compared to each other?
Both a response and a coping mechanism might be imperfect solutions; a coping mechanism doesn’t actually solve the problem, but there’s no guarantee that a response is necessarily going to be the right one. On the other hand, a response is likelier to have an impact with regards to the problem. Say you’ve got a character who’s afraid of spiders, but who’s just blundered into a room crawling with them. His muttering to himself that it’s not so bad, or telling spider jokes, or reciting a comfort phrase over and over would be a coping mechanism—running away, or stepping very very carefully, or stomping around him as if his life depends on it, would be a response.
Responses are likelier to be direct and literal; a coping mechanism is likelier to be symbolic, sort of a way to channel mindset. On the other hand, coping mechanisms can get away with making less sense than responses, due to their connection with the character’s mental processes.
Responses and coping mechanisms aren’t entirely mutually exclusive, though; some people will find ways to incorporate one into another. For instance, Tuyet’s snark reflex is a combination coping mechanism and response; it distracts her from her fear by giving her and her allies something else to think about (since she’s usually mindlinked with her allies, this is useful), and it has the useful side effect of occasionally annoying her foes into doing something more stupid than they might otherwise in order to get her to shut up. It’s rare for an action to be perfectly balanced between coping mechanism and response; more often, it’s a coping mechanism that happens to have a possible (if small) impact on the actual problem, or a response an aspect of which happens to have a secondary psychological benefit to the character.