Active and Passive
It's all to do with how they keep the engine noise out. Passive headsets form a sound-tight seal around your ears, which can be sweaty and uncomfortable.
Active headsets use fancy battery-powered electronics to feed negative engine noise into your ears, cancelling the real engine noise, with no need for the seal. But they do need batteries.
You probably wouldn't want to fly with an unreliable headset, so if you go for an active set, carry a spare set of batteries and learn how to change them on the fly.
Or better still, change them on the ground before you need to.