We study experimentally and numerically the synchronization dynamics of two laser modes, coupled by a coherent optical feedback injection. For a given coupling strength, we observe three synchronization regimes, depending on the initial detuning between the modes. If this detuning is sufficiently weak, the phase of the beat between the two modes remains constant. In contrast, for very large detuning, this relative phase drifts. Besides these two familiar cases, we identify an intermediate situation, in which the relative phase oscillates while remaining bounded. The frequency locking is preserved, even in the absence of phase locking.