I see this expression being used frequently and I think it would be helpful to parse the possible meaning by the person using it. Why? Because it has such a HUGE range of possible impressions that could be taken by the reader. Just to illustrate, I will place myself in the #1 category below of person who might use the expression "attempted suicide".
A. - At times you have felt such despair over life related problems, money, relationships or just general unhappiness that you have actually played out a scenario in your mind of how you would do it and included the imagined impact it would have on those who have hurt you as well as loved ones. You have never pursued the actual carrying out of the fantasy in any tangible way, i.e., buying a gun, tying a rope to a rafter, etc.
B. -Same as above but you have actually sat on the edge of the bed with a loaded gun in your mouth, or stood on a stool with a rope around your neck, etc.
C. - You actually 'attempted suicide' but survived. The rope broke, so to speak.