It's not two-phase
A two-phase power system has two phases 90 degrees out of phase. This can't be done with less than four wires. That's a lot of wires for not a lot of power transmission. Needless to say, this system hasn't gone very far.
Three-phase carries 1.732 x as much power on 1.5x as many wires as single-phase, so that is the system that is widely used for high-power applications.
What you're dealing with is actually single-phase, with a center-tap for neutral. This is called split-phase. Calling it 2-phase is incorrect.
The easiest way for a DC-electronics person to think of split-phase as neutral being 0V, pole L1 being +120V, and pole L2 being -120V. This won't lead you too terribly wrong as long as you remember it is AC, and so it's only true half the time :)
Neutral is what electronics people call GND or Vss. AC mains also has a "safety shield" which in that world is called ground, even though it never carries current except during fault conditions.
Small loads in the <=1500 watt territory attach to a 120V leg -- they connect to one phase or the other, and also neutral. A toaster might be hooked up between L1 and Neutral. A refrigerator might attach between L2 and neutral.
Large loads (>2000W) generally attach to both L1 and L2 legs - and enjoy 240V between them.
Neutral only handles "differential current".
It's common to put current monitors on L1 and L2, and not put any on neutral. It's easy to see what is moving on neutral; it is the difference in current between L1 and L2.
When the power monitor sees a 120V load, it appears as activity on only one pole - L1 or L2.
When the power monitor sees a 240V load, it appears as exactly equal activity on both poles.
Some loads (dryer, range) have 240V components and 120V components. The 240V parts of the load present as equal load on both poles. The 120V parts present as load on only one pole. So what you see in net is two draws that are large and slightly different. Examples are:
- Dryers, with about 20A of 240V dryer heating coil load and about 3A of tumbler motor load.
- Ranges, with 5-38A of various 240V range and oven heating coils and about 0.3A of controls, clock and oven light.