A green dragon has a breath weapon that deals poison damage. In addition to the MM entry, this is an example given in the PHB Description of Damage types:
Poison. Venomous stings and the toxic gas of a green dragon's breath deal poison damage.
Dwarves have two types of protection from poison:
Dwarven Resilience. You have advantage on saving
throws against poison, and you have resistance against
poison damage (explained in chapter 9).
[The "explained in chapter 9" appears to apply to the definition of poison damage as quoted above.]
The question is: is the green dragon's breath "poison", so that dwarves get advantage on the Con saving throw to take half damage, or is it some other kind of effect that happens to deal poison damage, so that dwarves don't get advantage on the Con save, but still get resistance to any poison damage they end up taking from it?
I believe the same question applies to a spell like poison spray — is that a spell effect that happens to deal poison damage, or is it poison (or both)?
As an aside, the spell protection from poison states (in part):
target has advantage on saving throws against being poisoned
This is different from the dwarven resilience – it is advantage against being poisoned versus advantage against poison. That type of protection would not apply to the dragon's breath, which deals poison damage but does not impose the poisoned condition.
There's a reddit thread that suggests that the poison spray spell should count as poison for the purposes of this ability, but it's not especially well argued or authoritative.