And my confusion at post 42.
A-B, B-C, and C-A are ALL single phases. They are 120 degrees apart from each other. When you use just 2 legs, you are using ONE of the 3 phases, not 2.
The confusion is because you only see 3 wires, but really there are 6 wires coming out of the 3 phase generator. Start and Finish for each of the 3 windings. It's clear if you think of them tied together in a Delta.
It's confusing when they are connected as Wye. Each leg does look like it's 120 degrees apart, but, as one leg is going up, the other is going down. The net voltage is a true sine wave, but the voltage is reduced. For 120/208, It's 120 * the square root of 3 (1.732).
Forget about 180 degrees. There is no 180 degree signal in 3 phase.
The 240 at your house is NOT 2 phases, 180 degrees apart. It's single phase. There are 2 windings coming from a single iron core. The Finish lead of the first winding is connected to the Start of the second winding (and grounded), but both of them are still coming from ONE phase, also from a 3 phase line. The 3 lines you see on the pole from the power company.