Firstly, yes there is a difference.
Global Positioning System
GPS is short for Global Positioning System. It is the collective name for a group of satellites that are in orbit around the Earth. They were placed there by the US Government decades ago and made publicly available during the administration of President Reagan.
Using a GPS receiver (a small device that can send and receive signals from any satellite within range) you can get your precise location. This location is provided as a set of co-ordinates.
Using this information and the co-ordinates of your destination, many GPS receivers can 'guide' you to the destination using a compass-like arrow. In theory, if you have the GPS co-ordinates of your home, using a GPS receiver you can find your way home from even the remotest place in the world.
The GPS receiver has become a common item that is fitted to many devices, such as your mobile phone or the security system in your car. Many smartphones, such as the iPhone, have a GPS built-in. If allowed, applications can use this information to direct you to, say, the nearest Italian restaurant. Some digital cameras even have a GPS. They can use it record exactly where the photo was taken.
A sat nav (short for Satellite Navigation) is really some very special software that uses the GPS signal. It takes the co-ordinates provided by the GPS and combines that with a comprehensive map. Then, given a destination, the sat nav software will calculate a route for you to your destination. As the GPS signal is constantly updated, the sat nav can give you step-by-step instructions on where you are and when you need to make a turn.
TomTom and Garmin are probably two of the best known brands when it comes to GPS and sat nav equipment. TomTom is a European company, that mainly produces sat nav devices for motor vehicles along with software for smartphones. Garmin, and American company, have a much clearer product range: everything from aircraft GPS systems to GPS watches to help athletes improve their performance.
Both of these technologies are improving and advancing and it will be interesting to see how they evolve.