T-Mobile and Cingular share bandwidth in California and New York; elsewhere, the networks are typically separate. T-Mobile only allows roaming on Cingular in a very few areas, such as the Carolinas where T-Mo has no coverage of its own. Both are GSM, though Cingular does still have some analog cell sites in many areas of the country.
T-Mobile's network is 100% digital GSM. The technology exists for combination analog/GSM phones (it's called GAIT) but only Cingular, not T-Mobile, has ever offered phones with this capability. Digital signals don't reach as far as analog, which is one reason why T-Mobile phones get absolutely no signal in many rural areas.
T-Mobile offers far more minutes for the money than anyone else, though, which is why I've kept service with them despite the lack of coverage out in the boondocks.