The definition of a clause is a group of words that contain a subject and a predicate. The definition of a sentence is a group of words that contain a subject, a predicate, and a complete meaning. Therefore, a simple sentence is a clause, a clause is not always a complete sentence because it might not have a complete meaning.
In a complex sentence, you will have two clauses. One we call the "independent clause," one that could stand alone as a simple sentence because it contains a complete meaning, and one that we call a "dependent clause," one that does not have a complete meaning even though it has a subject and a predicate. Here is an example of a complex sentence:
When most schools closed because of the snow, ours stayed open.
The first clause is the "dependent clause" because it does not have a complete meaning, although it has a subject (schools) and predicate (closed).