It's understandable how to came to that assumption but it's incorrect.
A split phase system
**broken link removed**
https://en.wikipedia.org/wiki/Split_phase
A two phase system
There's no fancy picture here but I'll offer two simple quotes:
"Two-phase electrical power was an early 20th century polyphase alternating current electric power distribution system. Two circuits, or "phases", were used, with voltages 90 electrical degrees apart in time."
---snip----
"Three-wire, 120/240 volt single phase power used in the USA and Canada is sometimes incorrectly called "two-phase". The proper term is split phase or 3-wire single-phase."
https://en.wikipedia.org/wiki/Two_phase