VERY interesting. I wonder why my audio distributor told me this, and why my electrician was reciting "phase A, phase B" about 100 times? 
Most residential dwelling units in the US are fed from a single phase transformer with a split phase secondary winding. As others have said there is only 1 phase. A center tap of the single phase winding will become the neutral "The Grounded Conductor", where it is intentionally connected to Earth. From either Hot conductor, of the single phase winding, to the neutral conductor you will measure 120V nominal. And naturally from Hot to Hot 240V nominal. Thus a 120/240V 3 wire power source.
And as others have said the Hot conductors are called Legs, or they are called Line. Usually identified by "L1" and "L2".
The term phase "A" or Phase "B" comes from a multi-phase power system.
The typical Utility power company generators produce 3 phase 4 wire WYE power.
(3 separate windings with one end of each connected together making a Y connection.)
The 3 Hot output leads are 120 degrees out of phase with one another and are usually referred to as Phase A, B, and C.
In most commercial and industrial building the incoming Utility power is a 3 phase 4 wire WYE AC power system. 3 Hot conductors with 1 common neutral conductor.
LOL, now it is possible to use 2 of the hot phases, say A & B and the neutral to feed a single phase electrical panel.... In this instance one Hot leg would be called "A" phase and the other "B" phase, because they are infact 2 different phases. You could have this situation in a multi-story apartment building that has separate electrical panels in each apartment.
In this case the power feeding the electrical panel will be 120/208V nominal.