I disagree with the statement: “What you call "single phase" motor is really a two phase
motor.”
Unless other wise specified, the starting or auxiliary winding is used only during the starting condition. SPLIT-PHASE MOTOR used without qualification, describes a motor to be used without impedance other than that offered for the motor windings themselves, other types (Resistance-start, Capacitor-start, Permanent-split capacitor or two values Capacitor) being separately defined. When a short-circuited auxiliary winding is used, the name is SHADED-POLE MOTOR. See NEMA MG1 Standard.
In regard to the phases, this can not be a two phase motor; Per IEEE Std-100:
“TWO-PHASE CIRCUIT. A polyphase circuit of three, four, or five distinct conductors intended to be so energized that in the steady state the alternating voltages between two selected pair of terminals of entry, other than the neutral terminal when one exists, have the same periods are EQUAL IN AMPLITUDE, and HAVE A PHASE DIFFERENCE OF 90 DEGREES. When the circuit consists of five conductors but not otherwise, one of them is a neutral conductor. Note: A two phase circuit as defined here does not conform to the general pattern of polyphase circuits. Actually a two-phase, four wire or five wire circuit could more properly be called a four phase circuit, but the term two-phase is in common usage. A two-phase three wire circuit is essentially a special case, as it does not conform to the general pattern of other polyphase circuits.
TWO-PHASE FIVE-WIRE SYSTEM. A system of alternating-current supply comprising five conductors, four of which are connected as in a four wire two-phase system, the fifth being connected to the neutral points of each phase. Note: The neutral is usually grounded. Although this type of system is usually known as the two-phase five wire system it is strictly a four-phase five wire system.
TWO-PHASE FOUR- WIRE SYSTEM. A system of alternating-current supply comprising two pairs of conductors between one pair of which is maintained an alternating difference of potential displaced in phase by one quarter of a period from an alternating difference of potential of the same frequency maintained between the other pair.
TWO-PHASE THREE- WIRE SYSTEM. A system of alternating-current supply comprising three conductors between one of which (known as the common return) and each of the other two are maintained alternating differences of potential displaced in phase by one quarter of a period with relation to each other.”