Two mechanisms of two-color (ω+2ω) laser-induced field-free molecular orientation, based on the hyperpolarizability and ionization depletion, are explored and compared. The CO molecule is used as a computational example. While the hyperpolarizability mechanism generates small amounts of orientation at intensities below the ionization threshold, ionization depletion quickly becomes the dominant mechanism as soon as ionizing intensities are reached. Only the ionization mechanism leads to substantial orientation (e.g., on the order of <cosθ> ≳0.1). For intensities typical of laser-induced molecular alignment and orientation experiments, the two mechanisms lead to robust, characteristic timings of the field-free orientation wave-packet revivals relative to the alignment revivals and the revival time. The revival timings can be used to detect the active orientation mechanism experimentally.