Independent clauses are also called main clauses. Independent clauses are the most important. Independent clauses can be all by themselves in a sentence.)
Dependent clauses are also called subordinate clauses. Sub=below or less important. Dependent clauses cannot be all by themselves in a sentence. Dependent clauses depend on the independent or main clause.
Simple:
He likes Italian food.
(1 independent clause)
Compound:
He likes Italian food, and she likes Indian food.
(more than one independent clauses)
Complex:
Because he wants her to be happy, they are going to the Indian restaurant.
(dependent + independent clauses)
A comma splice or fused sentence is when you take two main clauses and put them together using only a comma.
A fragment is an incomplete sentence. It is a sentence that does not have a subject and a predicate. It does not have a subject + modified verb.