One way phrases and clauses differ is in how the nouns and verbs work in relation to each other. Within a clause, a noun functions as a subject and "does" a verb. The nouns within a phrase do not function as subjects, so they do not perform verbs present in the phrase.
Both nouns and verbs may be present within a phrase or a clause, so the appearance of either is not enough to define the writing component. Clauses may stand on their own as complete sentences or can, as dependent clauses, be part of larger sentences. Phrases, on the other hand, always exist as components in larger sentences. Clauses can express complete thoughts, while phrases can only express additional pieces of information in sentences. Another difference between the two is that phrases are sometimes found within clauses, but clauses are never found in phrases.