Nope, it's fact. If Commander was regular Magic, Commander products don't need to say Commander. After all, it is regular Magic. If you want to play Commander, the person you want to play with would immediately know you want to play Commander if you said "Do you want to play Magic the Gathering" Does that happen? No.
Ask anyone to teach you MTG. They will not teach you how to play Commander unless you specifically told them you wanted to learn Commander.