Is an executor of a will the same as the trustee?

No. An executor settles an estate according to the provisions in the will. A trustee manages a trust according to the provisions in a trust.

A trust may be set forth in a will. In that case the will must be probated with the executor in charge of the probate of the will. Once the probate process is completed the court will allow the trusteeship and officially appoint the trustee. Then that trustee will manage the trust according to the provisions set forth in the will.