I have a level 41 character in GTA online with 100 in Shooting and something low ("Clumsy") in Stealth.
When playing job missions I like to soften up the AI opposition by sniping them from a good vantage point as far away as possible. This means I'm often on top of a building/ crane/ boat/ hill and hiding behind a billboard/ low wall/ box/ rock at the edge of sniper visibility - in the middle of the night.
I'm using the standard sniper with suppressor, advanced scope etc. At the moment I'm lucky to get more than two (head)shots off before the AI identify exactly where I'm hiding and come at me. I'm guessing that the reason for my detection is my low Stealth points.
You would think that shooting people 2 blocks away in the middle of the night while hidden behind a billboard on the top of a build would count as "stealthy" but my Stealth stays stubbornly on "Clumsy".
Switching into "stealth" mode by clicking the left stick (PS3) only changes my characters standing position and causes them to move slowly. I know from playing the storyline that I could perform "stealth" kills like this - if I wasn't 2 blocks from my protagonists.
Going into cover and sniping seems to cancel "stealth" mode. Standing up in "stealth" mode when I could be hiding behind something seems foolish, counter-intuitive and bad for my health.
So what is the purpose of Stealth and how does it work?