In the last few years Apple has been releasing systems with an advanced Mini DisplayPort connection for monitors that allows for some advanced options such as using an iMac as an external display. This port has been adopted throughout Apple's line of Mac systems because it offers high-resolution video handling as well as other options like audio support for connecting to television systems.
In a recent knowledgebase article on the DisplayPort connection, Apple describes how to identify whether or not your system has a DisplayPort connection, noting the port's geometry as well as the symbols used to identify it, along with various Apple-supplied adapters that work with DisplayPort.
As with most other ports Apple has used (USB, FireWire 400, FireWire 800, DVI, etc.), DisplayPort has had a unique connector; but with the release of Apple's new "Thunderbolt" technology in the latest MacBook systems, Apple threw in a potential source of confusion by using the same DisplayPort connector.
The new port is backward compatible so it can still be used to connect to DisplayPort devices; however, only the new port can be used to connect to Thunderbolt devices.
This means that while you can physically connect a Thunderbolt device to a Mac with DisplayPort, the device will not work, but if you connect a DisplayPort device to a Mac with Thunderbolt, then the device will work.
The main warning here is to be aware of and avoid situations when setting up or troubleshooting devices where you might confuse the two connections when you need to use the Thunderbolt technology. These can include connections to new high-throughput storage devices (and future unreleased devices), or when troubleshooting new Mac systems by connecting them in Target Disk mode, which is supported on the Thunderbolt connection.