Is the following a compound sentence, and why? Please explain, clearly differentiating between compound predicates and contracted predicates.

We sang and danced.

Is the following a compound sentence, and why?

We sang and danced.

What I understood of compound sentences was that they are made of two independent clauses, connected by a coordinating conjunction or comma or semicolon. But the concepts of compound subjects and compound predicates got me all confused. How does a compound sentence differ from a sentence with a compound predicate or a contracted predicate? How can I clearly differentiate between compound sentences, compound predicates and contracted predicates?