Just for the sake of completeness, there is also something called a grant of administration with will annexed. This occurs when, for whatever reason, the executor is unable to gain the grant of probate. This might be because:
The appointment of the executor in the will may not have been correctly drafted;
The will may be valid but the deceased did not appoint an executor;
The executor may have died before the deceased or renounced;
The executor may have been passed over by the courts.
Letters of administration can then be applied for by someone else who would ordinarily be expected to carry out the testator's intentions as set out in the will, but they would not be called the executor.