We study numerically the synchronization of two multimode semiconductor lasers unidirectionally coupled in an open-loop configuration, focusing on the comparison with the results obtained in the single-mode case. Anticipative and isochronous synchronization, and their range of validity, are analyzed from the point of view of the total lasing output, and the synchronization between individual modes is studied. Selective injection is also examined and compared with global injection. In light of these results, message encoding and decoding via multimode synchronization is analyzed.