@LuckyGuy I have read 3 scientific books about suicide, so maybe I can answer this. But I hope I don’t come off as being too dry and insensitive.
When people get to the point of wanting to commit suicide, it usually because they are overwhelmed by their pain and can’t see any way out. They want to “end their suffering”, but it’s not in the same sense of the saying in question. Suicide is a way people try to stop feeling their pain, a way to run away from the pain. And in most cases suicidal people are willing to give up suicide if they are presented with a better solution to deal with their pain. Not to mention a lot of people give out signs that they are about to commit suicide to other people, consciously or unconsciously, so that someone would take notice and save them. Some people say vague things like the world is meaningless, some people kill themselves but not to the point of dying… This is all because it’s not human nature to end one’s own life. Suicide is essentially a last-ditch response to a lack of option.
And that doesn’t even take into account the kind of suicide called “passive suicide”, which is very unconscious and has less to do with the free will to choose not to suffer.
As far as I can understand the saying in the question, it’s more about being at peace with your pain. You still experience pain, but you choose not to let it rule your life. You are at peace with it, accept it and make the best of your life in spite of it. This is the total opposite of the mindset od suicidal people, who want nothing but the pain disappearing. They don’t want to deal with it or accept it as part of their life. In a way they let the pain influence their decision. And this is not what the saying means by choosing not to suffer.