It is important to realize that the length of a sentence really has nothing to do with whether a sentence is a run-on or not; being a run-on is a structural flaw that can plague even a very short sentence:
The sun is high, put on some sunblock.
When two independent clauses are connected by only a comma, they constitute a run-on sentence that is called a comma-splice. The example just above (about the sunscreen) is a comma-splice.