I started a thread on this a few days back and there didn't seem to be much knowledge yet.
I infer that not all poisons inflict the "poisoned" condition.
Per p. 105 of the Basic Rules, a poisoned creature has Disadvantage on attack rolls and ability checks. Also, it's only the basic poison that's +1d4 - surely a level 20 poison will have much more serious effects?
The one example we have is a spider whose poison specifically inflicts the condition. My take would be basic poison does not.
I presume it only applies once, as in every prior edition, and that there will be stronger poisons in phb or dmg.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.