I have found this Q/A ("Does damage from Armor of Agathys take place before or after a character takes damage from an attack that hits?") and also this Q/A ("What happens if a creature is killed between its attack and damage rolls") both of which use the idea that getting hit by an attack and taking damage from an attack happen at different times.
The armor of Agathys spell is an example of when this doesn't matter as it states:
If a creature hits you with a melee attack while you have these hit points, the creature takes 5 cold damage.
This effect does not require any sort of reaction, it simply happens simultaneously with the hit.
However there are features where the answer does matter such as the Sun Soul Monk's Sun Shield which states:
If a creature hits you with a melee attack while this light shines, you can use your reaction to deal radiant damage to the creature.
This requires your reaction, and we know that reactions (typically) happen after their triggers as supported by this Q/A ("Do reactions interrupt their triggers or not?") so the Sun Shield effect definitely happens after you are hit (making it a distinct scenario from armor of Agathys).
But are getting hit and taking damage simultaneous events?
If yes, then the reaction would occur after the hit and thus after the damage.
If no, then the reaction would occur after the hit but before the damage.
When the reaction can occur is important.
Let the Monk have only 1 HP left and be hit by an attack from a creature.
If they are hit and take damage simultaneously, then they would fall unconscious and be unable to take the reaction.
If the hit happened before the damage they could take their reaction, dealing damage to the attacking creature, and then take the damage, falling unconscious as a result.