How poison works exactly?

[tinkthank]

I've seen conflicting information here in my searches, so I will try to ask very explicitly.
There seems to be weak, strong, and death poisons, perhaps there are others. But all I can see when a unit with a poison weapon strikes another is a little green bar underneath the wounded unit.
If this is understood analogously to the bars of fatigue and HP, the unit would be fully poisoned when it extends completely to the right. Yet I am unsure what this actually means, since one can see completely "greened" units up and about.

So does "strong, weak or death" simply have an effect on what happens after the green bar is fully extended, or the rate or intensity in which the green bar extends, or both?