倒れる and 倒す: falling over and tilting something down
Compare an object falling with knocking it over, and distinguish reclining a seat from defeating an opponent.
What fell over
強い風で自転車が倒れました。 says that a bicycle fell over in strong wind. With 倒れる, read たおれる, the bicycle is the subject.
机にぶつかって、花瓶を倒してしまいました。 says that someone bumped into a desk and knocked over a vase. 倒す, read たおす, can describe an accident rather than deliberate action.
Tilt something intentionally
座席を少し後ろに倒してもいいですか。 asks permission to recline the seat a little. It concerns tilting the backrest, not damaging the seat.
倒れた看板を二人で起こしました。 says that two people raised a fallen sign. 倒れた gives its state, while 起こした describes changing that state.
People and competition
人が急に倒れました。 reports that someone suddenly collapsed. The sentence alone does not identify the cause or their medical condition.
決勝で強い相手を倒しました。 can mean defeating a strong opponent in the final. In a competition, 倒す need not describe physically knocking someone down.
Does 座席を後ろに倒す describe damaging a seat?
Show the answer and why
In a seat-adjustment context, it means reclining it. The object and situation determine the specific sense of 倒す.