“The big difference is that MO have a hashkafa for being MO. They are, generally, Bisheeta MO.”
That’s not a real difference l’maaseh. If they behave in a way which–today–we call “MO,” then I don’t really care what their kavana is, they’re MO. Labels are our friends. They tell us who’s kashrus can be trusted, to which shuls we can go, etc.