And what is the difference between coordinating and subordinating conjunctions? Is one kind of sentence (compound or complex) characterized by either a coordinating or subordinating conjunction, while the other kind is characterized by the other?
Yes, this is a good place. It's simple, really.
There are two ways to combine clauses. One of them is simply stacking together sentences, like
This is a compound sentence (not "compound clause", by the way); it contains only clauses that are linked together by the coordinating conjunctions and, or, and but. Compound sentences can be reduced by Conjunction Reduction, producing, for instance
Compound sentences are easy; all the sentences are on the same level as main clauses, and none of them modify another clause.
Complex sentences — the other way to combine clauses — are not easy. A complex sentence has at least one subordinate clause, and there are a lot of different kinds of subordinate clause, each with their own set of rules and their own set of idioms and connotations.