They are different, and they have different uses.

PHRASE: a group of related words that does not contain both a subject and a finite verb.
Example: The woman in the fake-fur coat
Example: Having survived the storm

CLAUSE: a group of related words with subject and a finite verb.

Independent clause: a clause that could function as a sentence if left alone.
Example: The woman in the fake-fur coat survived the storm

Dependent clause: a clause that could not function as a sentence if left alone.
Example: If the woman in the fake-fur coat survived the storm

Finite verb: a verb that is not an infinitive (to survive); not a participle (was surviving); and not a past participle (has survived).
Examples: survive; survived.