In public, after a drink, people can be a bit tipsy, for your benefit, I'll explain, that means walking properly, not bothering anyone, and not stepping out on the road without looking etc, no problem with that.
Incapable, drunk to such a stage that he is staggering, bumping into people, shouting insults at them, not looking before crossing the road etc.
If you want me to explain the "etc's" I won't bother. Is that plain enough for you?