We report on the study of the linear and circular magnetogyrotropic photogalvanic effect (MPGE) in GaAs/AlGaAs quantum well structures. Using the fact that in such structures the Lande factor g* depends on the quantum well (QW) width and has different signs for narrow and wide QWs, we succeeded to separate spin and orbital contributions to both MPGEs. Our experiments show that, for most QW widths, the MPGEs are mainly driven by spin-related mechanisms, which results in a photocurrent proportional to the g* factor. In structures with a vanishingly small g* factor, however, linear and circular MPGE are also detected, proving the existence of orbital mechanisms.