First, the Trustee is usually designated to the creators of the trust. While still living, the trustee can make changes to the trust.
Trusts are normally revocable and can be canceled while the original trustee or trustees are living. After the trustee dies the trust becomes irrevocable.
Second, the Successor Trustee is designated to assume legal control over the rust and has all the power that the original trustee had. Successor Trustees become the trustees upon the death or resignation of the original trustees.