It's that simple. A clause is a group of words including a verb and its subject. A phrase is a group of words that does not include a verb and its subject.
Some clauses are sentences.
It does not matter how long the phrase is. If it's a phrase, it is not a sentence. BOTH types of clauses include a verb and its subject. If the group of words does not include a main clause, it is not a sentence. If a group of words does not include a main clause and you set it off as a sentence, you have generated a sentence fragment.