There are two different (but similar) ports that appear on different Macs that often get confused. They are the Mini DisplayPort and the Thunderbolt port. Please take a look at the picture on the right to refresh your memory as to what they look like.

As you can see the plug is exactly the same but the icon that is beside each is different. The Thunderbolt port is on the left and the Mini DisplayPort on the right. In the past, the Mini DisplayPort was used as an audio/video output port which was used to hook up your Mac to an external display or monitor. The new Thunderbolt still does this and is backwards compatible with Mini DisplayPort adapters. The main difference between the two is that Thunderbolt can also transfer data (backing up or transferring files, for example) by using adapters to USB, Ethernet, FireWire or directly to another Thunderbolt device. This means you can have a working connection when plugging in a Mini DisplayPort peripheral to a Thunderbolt port but not vice versa. See the image below for a better understanding.