Magnetic refrigeration has the capability to be a breakthrough technology in the field of refrigeration at room temperature and it has been recently addressed as one of the major promises in theme of energy savings. Several magnetic refrigerator prototypes have been developed by research groups, according to different embodiments and process thermodynamics. This short study follows an idealized line connecting, from a conceptual rather than historical point of view, the different geometries and embodiments, and proposes a classification of magnetic refrigerators based essentially on the type of magnetic source, the regenerator material and arrangement, the heat transfer fluid and the relative motion among the active elements of the device. This ordering is then applied to several actual prototypes, showing the potential of the proposed method to give a comprehensive description of magnetic refrigeration devices by means of a few digit string.