Apple made two similar 27" displays.
- The Apple Thunderbolt Display (27-inch) (model A1407) has a hydra cable with TWO heads: Thunderbolt (Mini DisplayPort connector) and MagSafe. It requires Thunderbolt input.
- The LED Cinema Display (27-inch) (model A1316) has a hydra cable with THREE heads: Mini DisplayPort, USB-A, and MagSafe. It requires DisplayPort input.
Another difference between the displays is that the Thunderbolt Display has FireWire 800 and Gigabit Ethernet hub ports. The LED Cinema Display does not.
The Apple Thunderbolt 3-to-2 adapter is appropriate for connecting a Thunderbolt Display, but not for connecting a LED Cinema Display. A third-party USB-C (male) to Mini DisplayPort (female) adapter is appropriate for connecting a LED Cinema Display, but not for connecting a Thunderbolt Display. You must match not just the connectors – but the type of signal being carried over those connectors.