So this is different from a 3 phase system (N L1 L2 L3) with 120 degrees shift between the lines? It is instead basically a 2 phase system N L1 L2 with a 180 degree phase shift between L1 and L2?

I was already confused with the 240 being mentioned somewhere in this thread... it becomes a bit clearer now.

Not an electrician, but yes (I think).

https://en.wikipedia.org/wiki/Split-phase_electric_power

Most US residential housing is fed off a 240V center tapped transformer. Center tap is connected to ground and neutral at the breaker panel. That gives you two 120V phases to neutral. And 240V from phase to phase.

In the breaker panels the phase alternates as you go down the rows of breakers. So you can install a dual breaker for 240V. Typically only large appliances like stoves, water heater, driers, and air conditioners are 240V. Everything else is 120V.

I heartily recommend a three phase induction stove. 400V of cooking power (mine is rated at something like 8kW…?). Carbon steel pans get ready in seconds.