When we forgive, we tend to let go of most or sometimes all of our anger. When we let go of our anger we do not necessarily forgive. For example, we can let go of anger and dismiss a person as unworthy of our respect or love. Forgiveness, on the other hand, strives to respect and love those who have hurt us. Forgiveness never condemns a person for an unjust act. At the same time, forgiveness does acknowledge unjust acts as wrong.
For additional information, see Forgiveness Defined.