The WAAS system uses a number of ground GPS receivers. These receivers pull the GPS data off the L1 GPS signal. This location is compared to the real location of the receiver. The difference between the slightly inaccurate GPS L1 derived location and the highly accurate known position of the receiver is used to compute the error of the GPS system.
The error is then used to compute a correction. That correction information is uplinked to two non-gps satellites, one over the west coast, one over the east coast. That correction information is then broadcast out from those satellites to WAAS enabled GPS receivers. The GPS receiver takes it's GPS derived location, which will normally have a bit of error in it. It uses the WAAS correction information to increase the accuracy.
DGPS is a similar sort of system. Instead of uplinking the correction data to satellites, the correction data is instead broadcast out over long wave transmitters located at different locations. Again, a DGPS enabled receiver picks up the correction data and uses it to produce a more accurate GPS signal.
Sort of strange, when you think about it. The DOD purposely degrades the consumer GPS signal so it can't be used for military use. The US Government (FAA and US Coast Guard) spend more money sending out correction signals to make it more accurate.
As for why you can't pick up the GPS signal on your scanner, it has a lot to do with your antenna. A GPS antenna is a very high gain antenna specifically designed for the 1575MHz signal. I've got GPS timing antennas at work, some are 28dB gain, others are 40dB gain. The antennas use a circular polarization to match what the GPS satellites use. Your scanner antenna is much lower gain, probably vertically polarized, and oriented to pick up signals from the horizon. To top that off, 1575MHz is going to suffer a whole lot of loss in your feed line.