What's mentioned as running now (EGNOS) is a wide area variation of differential GPS. It uses a number of base stations to check the accuracy of the received GPS signal, then transmits the variance to users via Inmarsat and a couple of other geostationary birds. Just a bigger version of the technique used by most airports and civil engineering sites now.
Galileo will be a Eurpoean constellation of satellites similar to the US based GPS system which is politics driven, in that some people are scared that the USA will turn off, encrypt, or drop GPS at some point.