I see your point too, johnqh. I also think the difference is, the wedding coordinator is a very detailed oriented person who handles the schedule. If you`re running errands for the bride, you will be at their `beck and call`, which will probably be much more difficult to schedule.
Another point, you will need to be a person that they feel comfortable with and that they can trust, which is something you will have to really sell about yourself. As you mentioned before about bridezillas...these gals will need you to take care of what they feel are VERY IMPORTANT ERRANDS., as in picking up their dress from the seamstress, getting it pressed, delivering and picking up items that have to do with their big day.
I think, if you plan to do this, you should work with an excellent coordinator that recommends them, to use your service.