How does stealth work in Far Cry?

I recently picked up Far Cry Classic on the Xbox 360. After playing through a few levels I became frustrated with guards always spotting me. This included such things as seeing me in a dense jungle or through a large rock. It seemed to only require that a guard was facing my direction in order to see me, regardless of obstacles between us.

Additionally, the red/orange/yellow/green indicators also seem to be somewhat frustrating. For example, if I fire a sniper rifle from a few hundred metres and then quickly move to a new location the guards seem to stick to a certain indicator. Nearby guards will rush to the location I fired the gun, and remain in that position with a mix of yellow and orange indicators. I sat nearby for over ten minutes but the guards never moved or changed colour.

In other scenarios, if I turn a guard orange by being almost spotted I can quickly escape so that he turns back to yellow and then green.

I enjoyed the original release on the PC over ten years ago, and remember playing through some levels by using stealth. I downloaded the first game on Steam but it seems to have the same problems as the console versions (this version is titled Far Cry rather than Far Cry Classic, and still has the older graphics).

So how does stealth actually work in the newer versions of the game? Any insight to allow me to play through some levels using stealth (i.e. either sneaking through outposts/camps/patrols or picking off guards)?