I think Thomas Joiner in Why People Die by Suicide is instructive in explaining the "regret" of suicide attempts. He asserts that individuals will frequently frame a suicide attempt as an impulsive act. This, he suggests, is done to avoid the shame and social embarrassment that it was a slow, deliberate decision. He notes that even seemingly impulsive attempts may function as a form of priming, gradually reducing the fear response for the eventual act that takes their life. When considered against the potential consequences that arise from admitting to methodical planning (extended psych ward visits or increased scrutiny from medical professionals, as examples), Joiner's conclusion appears to be logically founded.
Extending Joiner's argument a step further, while acknowledging the obvious limitation that we cannot know the experience of the dead, it is possible to recontextualize the regret following a failed attempt. Some survivors (and likely a greater number who do not admit to it because of the consequences) claim they did not regret the act itself but regret that they were not successful, especially among those who continue to believe that life holds more suffering than death. For these individuals, the regret experienced during or immediately following the attempt could be the result of two factors: knowledge that the attempt ceased to result in immediate death, condemning the individual to the prolonged suffering they were seeking to escape, and/or an awareness of the consequences that follow such an event should they not succeed, such as permanent injury. That being said, this is not a complete theory; there are people who genuinely recognize that they did not wish to die following a suicide attempt who do not fall under this classification.
In reference to the original question, this dilemma makes it difficult to know if it is the result of a genuine change in a person's state of mind or the consequence of survival instinct. If someone is markedly depressed and/or has had repeated, serious suicide attempts which they've failed and display continued dissatisfaction with life, it'd be easy to classify it as the latter; by comparison, if they've found an appreciation for life after attempting, it may be that their attempt was an unfortunate coping mechanism which carried the possibility of death, whereas the regret they experienced stems from the genuine change in their state of mind clashing with the horror of what they did. It's unfortunate, then, that we can only know which side we fall on when we're right up against the ledge between life and death. Even then, people may simultaneously find themselves on both sides to a varying degree. That middle point is where I'd class myself, incredibly dissatisfied with life and part of my regret comes from being stuck in a state where death is prolonged, but part of it comes from a desire to keep living despite the pain.