GNSS = global navigation satellite system , which is the 'generic' term
GPS = global positioning system, which is the version built by the US DoD; has two services, a standard service (L1), and a precise service (L2). Most people (well, at least, in the circles I run in, of Americans) refer to GPS as if it's the generic term for all of the GNSS.
GLONASS = the Russian sat nav system. Some units now use both GPS and GLONASS signals, not just GPS. This is especially useful in Alaska (I've got friends there that have a limited exposure to the GPS constellation, but the GLONASS constellation has better coverage across the northern latitudes).
The EU and China are both working on similar systems; Galileo and Beidou (Compass), respectively.
A lot of cell phones use AGPS = Assisted GPS. This combines a GPS position with a location based off cell-tower locations, to improve the accuracy. (That's why I can be sitting on the couch at my house and my iPhone will plot my location right on my house, where my high-end Trimble units might not get a high-accuracy fix under a leaf-on tree canopy).
A lot of high-accuracy Trimble units don't seem to be as accurate, because they're more picky about signal quality, and have a hard time getting a fix when a Garmin might lock in right away. But, the Garmin can only calculate its location and record that; the Trimble saves all of the data used for making the calculation, which you can later post-process against a basestation, and have a more accurate location.
The US originally had Selective Availability, SA, which would intentionally vary the accuracy of a GPS location, for 'protection of military targets'. However, SA was turned off in 2000, and hasn't been turned back on.
One other thing to mention: it's possible to jam a GPS signal. It'd be possible for the US to jam signals near bases, it'd be easy to do if they wanted to; and, the AGPS system should correct some of that back out, lessening its impact - if it existed. Could be as simple as, the AGPS was just more accurate than a non-AGPS system.
While I'm at it, WAAS is Wide Area Augmentation System; it was started for the FAA, to improve GPS accuracy for aircraft coming in for landings. There are a bunch of stations across the continent, constantly reading GPS locations, but they know their precise location, so, they calculate a correction factor. All of these stations' results are turned into a data layer that two satellites broadcast out; if you're picking up a WAAS signal, your unit can use that to improve the accuracy of its calculation of your location. However, if you're elsewhere... say, in Europe, and have WAAS turned on, it would actually degrade your accuracy, as the correction is targeted for the continental US.
FWIW....
