So, I'm just curious - If I change the difficulty setting, what specifically changes? I can imagine several different possibilities (e.g., enemies get more health, they deal more damage per attack, my attacks deal less damage to enemies, enemies spawn more frequently, etc.), but I don't know what is actually changing.

It just changes how much damage you actually deal and how much damage the enemy deals to you. The lower the difficulty, the harder you hit and the weaker the enemy hits. The higher the difficulty, the less damage you deal and the more you take.