“What does the phrase “sentence commuted” mean? Am I correct that it means that the original sentence is complete?”

A commutation does not necessarily mean that the sentence is complete, though it may have that effect. The term commutation refers to a reduction in the sentence, usually imprisonment (though it can also include the reduction of court ordered penalties or fees), for a crime you have been convicted of. Even though a sentence may be commuted, or “reduced”, the conviction is not erased, as would be the case with a pardon. Commutations of sentences are handled by the executive branch of state or federal government (depending on the crime), meaning that either the President of the United States (federal crimes) or governor of your state (state crimes) must have issued the commutation.