A babysitter is an outside contractor who comes in your home to provide service, like a plumber. A home-based day care takes money at that address for services provided to someone else who drives to that address and receives services at that address.
I understand your point, but I don’t know if there’s that clear a distinction between the two. When I was a kid my siblings and I were occasionally dropped off somewhere else for babysitting. Would that constitute a home-based business under HOA rules or a state or municipal law?