No. When a child is adopted, all parental rights and responsibilities transfer to the adoptive parents. In foster care, children continue to be a part of their own family and the local authority that is responsible for them may share parental responsibility with their parents.
In many cases, fostering is a temporary way of providing a home until children can return to their own family, or move into an adoptive family. However, for some young people this is not appropriate and they will stay in foster care until they move on to adult life.