The difference between an Active and a Passive DisplayPort adaptor is a circuit that makes the conversion happen. Active DisplayPort adaptors have a chip that makes the conversion happen while passive DisplayPort adaptors do not.
will handle the conversion for you and as such you can get away with using the much less expensive Passive adapters.
Thunderbolt connectors are the same as mini-DisplayPort connectors and they ALL support Dual Mode DisplayPort so if you are going from Thunderbolt to HDMI, you can use the much less expensive Passive DisplayPort adaptors
If you are running multiple screens you will often find that Passive DisplayPort Adapters will not work. If you have a Microsoft Surface or SurfaceBook, you will often find that Passive DisplayPort Adaptors will not work.