I think it depends on every babysitter.And one varies from another.
Some may tell you what they will do but may end up just doing routine care.
Others may tell you and carry out what they plan.You will be able to tell if your kid is learning anything.
For infant care centers
Most have structured programmes for them especially for the older infants.They will have stories,sing a long,craft, life skills(self feeding)
However there are others too who just do routine care.