Incontinence of stress is when leakage occurs during laughter, sneezing, coughing, etc. Usually, those with stress incontinence do not recognize it as a medical condition. In most cases, stress incontinence is not dangerous and can often be treated through retraining of urethral muscles.
Incontinence of urge, however, is when you feel the sudden need to urinate and cannot help but have an accident. This is caused by losing the first message sensation telling you that you need to urinate.
"Grant me chastity and continence, but not yet." (Da mihi castitatem et continentiam, sed noli modo.) - Saint Augustine
Aristotle in Book VII of Nicomachean Ethics described incontinence as knowing virtue, but not having habituated it to control passion. For example: Though I know courage is a virtue and understand the benefit to my situation, I am a coward because I have not habituated courage and can't control of my fear. [Aristotle: Nicomachean Ethics, Book VII] Plato/Socrates reasons that there is no such thing as incontinence because the only reason a person would choose a path that is detrimental to oneself is for lack of knowledge/experience. [I don't remember the reference]