Three Types of Harm - and One More
All these reduce EL, but Hindrances don't count toward being Down; they are situational obstacles, not damage.
Hindrances can't be recovered at all. They must be dealt with through the story, be they Blindness spells, being bound with ropes, or any condition that requires specific narrative action to remove. That is both good and bad, because it means you can get rid of them in the middle of a fight, but healing magic and similar assistance doesn't apply to them (unless it does.)
Complications disappear completely on any successful recovery roll. Think short-term fatigue, vertigo from a head blow, a numbed limb, or losing your nerve after a good scare. "Wait, what? How does 'losing my nerve' count as damage?" It reduces your effectiveness, it's something care can fix, and most importantly, it can take you out of a fight. If something convinces you to quit, then it applies. Powerful illusions can count as Complications; if you think you are dead, you pass out, but given time and care you will wake up and realize it wasn't real. A successful intimidation attack that shakes your confidence is as good as a crack to the head.
Injury requires daily recovery rolls and heals slowly over time. Bruised ribs, sprained ankles, bleeding gashes, and broken bones are certainly real damage that can put you out of commission.
A Clarification
It is important to understand that Harm does not mean damage. Harm is anything which impedes a character, or takes away their agency. Psychological Harm that results in ongoing loss of confidence can be as debilitating as a broken leg. Social Harm that affects a character's reputation can certainly make them less effective in many situations, though if the character doesn't care about such things, the GM should be careful to apply something that would matter to them. Most of these can and should still be handled with the usual rules.
Still, it is possible that the result someone takes from losing a resistance roll is an Imposed Hook. See the section on Hooks for more info.