A new unified adaptive flux observer for induction machines (IMs) and permanent magnet synchronous machines (PMSMs) is proposed in this work. The proposed unified observer is created using both the well-known "Voltage Model" (VM) and the "Flux Model" (FM) in the estimated rotating synchronous frame. Under the time-scale separation assumption between the rotor flux dynamics and the stator current dynamics in the estimated rotor synchronous frame, the rotor flux can be considered a slowly varying signal for which an adaptation law has been designed. We showed that the proposed unified observer can be applied to IMs and PMSMs with minimum knowledge of motor parameters, requiring only information on the stator resistance and $dq$ axis inductances. The stability of the proposed observer is proven using the Lyapunov theory based on the presented unified model. Finally, numerical simulations in MATLAB/Simulink and experimental tests on an IM and a PMSM are provided to illustrate the theoretical results.