How does a two-phase system differ from a three phase system?

A two-phase system is archaic and you are unlikely to find it in use anywhere these days, so it is mainly of historical interest. A two-phase, three-wire system, consists of two phase voltages, displaced from each other by 90 electrical degrees, and a phase voltage which is 1.414 x phase voltage.

A three-phase system consists of three phase voltages which are displaced from each other by 120 electrical degrees. In the case of a three-phase, three-wire, system, the line voltages are numerically equal to the phase voltages; in the case of a three-phase, four-wire, system, the line voltages are 1.732 x phase voltage.