The statement "This car's not working" is a clause.
A clause is a collection of words that has a subject that is actively doing a verb. This means a clause has a subject and a verb.
As seen in the statement, "This car" is the subject and "working" is the verb. Another example is . "Because she smiled at him". She is the subject and smiled is the verb.
A phrase on the other hand, is a collection of words that may have nouns or verbals, but it does not have a subject doing a verb. A phrase is not a sentence because it does not have a complete meaning.
Examples:
All right reserved and a story as old as time.