Piaget's stages focus on cognitive abilities and Erickson's on moral development. Both are related, because children need to reach certain intellectual stages before they can reach moral ones. For example, in order to empathize with others, children have to have awareness of others. Deeper moral thinking requires the ability to think abstractly.
Piaget's basic argument is that kids develop cognitive abilities as they grow older. Until they get to certain stages of development, they are not capable of the sorts of tasks that require the abilities that go with those stages. So, in other words, it would be pointless to try to teach certain things (like abstract ideas) to an 8 year old (no matter how smart they are) because they haven't reached the stage where they can learn that.