I don't have much time (taking a break), but I'm afraid Erik is right and you got this really wrong. I'm not even sure why; I thought this was quite clear.
KRAD, as in Kraftrad, is the higher-order category and Motorrad the subcategory. Here is a reference (if it's yours, jccantrell, tell me, though I don't think so):
https://kfz-innung-schwaben.de/fileadmin/resources/intern/te...See p.2, where it says: "KRAFTRAD O.LB.," then "alter Führerschein" and
"KRAFTRAD O.LB.
KRAD, MOTORRAD O.LB
KRAD, M.BW, MOTORRAD O.LB
KRAD, ROLLER O.LB
KRAD, M.BW. ROLLER O. LB"
See what I mean? Basically, there are two defs of KRAD, one being the "generic" one Eric provided and the following: "...mit einem Hubraum von mehr als 50 ccm oder mit einer durch die Bauart bestimmten Höchstgeschwindigkeit von mehr als 45 km/h (vgl. § 2 Nr.9 der Fahrzeug-Zulassungsverordnung)..."
https://wirtschaftslexikon.gabler.de/definition/kraftrad-kra...Light motorcycle doesn't even factor in here somewhere. The above references the following:
https://www.gesetze-im-internet.de/fzv_2011/__2.htmlNothing to do with mopeds either.
Best