We present a comprehensive study of dual optical parametric oscillation (OPO) within one cavity, which is commonly used as the pump source of terahertz (THz) wave difference frequency generation (DFG). The growth of two output wavelengths with the OPO input energy is not synchronized, due to the competition. This phenomenon is analyzed experimentally and theoretically, to our knowledge, for the first time. A two-stage growth of the product of dual-wavelengths' energies (also the output of THz-DFG) is predicted: first as a line and later as a parabola. With a homemade organic crystal, monochromatic THz-DFG is achieved under the pump of this dual-OPO. A tuning range up to 30 THz and a highest signal-to-noise ratio of 600:1 (27.8 dB) are obtained at room temperature.