Is there a difference between “damage taken” and “damage dealt”?

This question is prompted by parts of How much damage can the Guardian of Faith spell deal?, If someone casts Vampiric Touch on a creature with necrotic absorption, does the caster take damage?, and this answer.

I am hoping for a more conclusive understanding of whether, within the mechanics of 5e, there is a difference between damage taken by a creature and damage dealt to a creature.

Is there a difference between any of the following aside from phrasing:

  • Gaspar took 8 points of damage from Joan’s attack
  • Gaspar was dealt 8 points of damage by Joan
  • Joan’s attack against Gaspar dealt 8 points of damage

Or rather is there a difference between "A creature hit by your attack takes 1d8 points of damage" and "Your attack deals 1d8 damage to the creature it hits"?