The advancement trigger entity_hurt_player is triggered when the player receives non-entity damage (like fire) as well but the trigger entity_killed_player is only triggered if the player is killed by an entity.
Note: If both triggers should trigger for non-entity damage as well it might be good to rename them to something like player_being_hurt and player_being_killed.
- Download the attached datapack MC-116922.zip and place it in the datapacks directory of your world folder
- Load the world (or if it's already opened run /reload)
- Take fire damage
→ You get the advancement "Taking damage"
- Die because of fire damage
→ You do not get the advancement "Being killed"