Phrases and clauses are both groups of words, but there is a difference between them.
A clause is a group of words that includes a subject and a verb.
Andrew played his guitar. (The subject of the sentence is Andrew, and the verb is 'played'.)
A clause can be a whole sentence or part of a sentence.
The mouse ran away. (one sentence with one clause)
Peter slipped on the ice and his sister laughed at him. (one sentence with two clauses)
A phrase is a group of words that form a chunk of a sentence. A phrase may contain nouns or verbs, but not both.
the little kitten (noun phrase)
may be going away (verb phrase)
One way of thinking about the difference is to say that clauses are made up of phrases.