All-optical magnetization switching has been studied extensively in recent years. A typical form of non-thermal magnetization control is the inverse Faraday effect (IFE). It involves rotation of the linear polarization of a probe pulse induced by a circularly polarized pump pulse in a transparent medium. Recently spin precession accompanied by the IFE has been reported by Kimel et al. in iron compounds. The interpretation of this phenomenon is that an effective magnetic field pulse parallel to the pump wave vector is induced by the circularly polarized light pulse, giving rise to the precession. The same effect has also been observed even in pure antiferromagnetic NiO with no net magnetic moment in the ground state [1,2]. Spin precession is also triggered with a linearly polarized pump pulse, in particular, a pulse polarized in a direction non-parallel to the crystal axes. This phenomenon is called the inverse Cotton-Mouton effect (ICME). In the majority of previous publications, however, the excitation of spin oscillations by ultrashort laser pulses was associated with IFE and ICME separately. We study spin precession in orthoferrite with a pump-probe technique as functions of the pump pulse polarization and wavelength [3]. We found that both effects, IFE and ICME are working in the same way, exciting the same mode of spin precession. The initial phases of the spin precession via IFE and ICME differ by 90 degree, allowing the two effects to be distinguished. We found an essential dependence of the phase on the pump wavelength and demonstrated that the IFE and ICME are dominating effects in different spectral regions, in the visible region and in the near-infrared region, respectively. Thus, the analysis of the phase difference of the spin precession reveals the mechanism of coherent spin manipulation by ultrashort pulses.