K.W.
I would say a nanny is employed by a family and watches that couples children on a daily basis in their own home, sometimes the nannies will live in the home with the family. A nanny will feed your kids, clean up after them, etc, its very personalized b/c they spend so much time with your kids. The family would negotiate the nannies duties with her when she is hired.
A babysitter is someone you call here and there, whenever you and your husband want to go out, to keep your children.
A childcare provider is a licensed business that you drop your child off at while you go to work, they keep many people's children at once. Your child is fed, etc while they are there too.
Some folks interuse the words, i.e. call their kids daycare the babysitter, etc.