The mechanism of the terahertz (THz) wave generation (TWG) in dual-color fields is elucidated within the theoretical framework of single-atom based strong field approximation (SFA). Evaluating the transition dipole moment, the continuum-continuum (CC) transition, rather than the continuumbound recombination for the high-order harmonic generation, is confirmed to be the core mechanism of the TWG. The analytic form of the SFA-based CC description is consistent with the classical photoelectric current model, establishing the quantum-classical correspondence for the TWG. The theory is supported by parametric dependence of experimental THz yields calibrated by the joint measurement of the third-order harmonics. Present studies leave open the possibility of probing the ultrafast dynamics of continuum electron.