I agree, that is very well put.
That's why I hate when someone just mindlessly says "most people regret it after a suicide attempt." It doesn't take into account the context whatsoever. Very few people are going to be calm and happy while committing suicide especially if they are not using a peaceful method, and during that time the survival instinct will take over, emotions are high, and the brain can convince you of anything to make you want to live.. and then when that moment is over, you're back to where you started from wanting suicide again. People will ""save"" someone from a suicide attempt and then not give a shit when whatever made them want to commit suicide in the first place still hasn't been solved or can't be solved and leave them to rot, or try again later. I don't know if the suicide statistics ever follow up with people after an attempt to see if magically their suicidal thoughts have disappeared or if they ever try again and succeed. I haven't seen that much.
In the case of "they just want the pain to stop" wanting the pain to stop is the equivalent to wanting death for me, because that is the way for the pain to stop, and for many people that is the only way. Because any alternatives are physically impossible, and despite what many people thinking sitting around for the rest of your life waiting for a miracle is a fool's errand.