The others were the non-wireline carriers . Each company in each area took half the spectrum available. The nonwireline carriers usually got the A Band and the wireline carriers got the B band. There's no real advantage to having either one. It's important to remember, though, that depending on the technology used, one carrier might provide more connections than a competitor does with the same amount of spectrum.
Mobiles transmit on certain frequencies, cellular base stations transmit on others.
A and B refer to the carrier each frequency assignment has. A channel is made up of two frequencies, one to transmit on and one to receive. Actually, the strange arrangement of the expanded channel assignments put more stringent filtering requirements on the A band carrier, but it's on the level of annoying rather than crippling.