A run-on or fused sentence is two independent clauses which are not separated by any punctuation.
Run-on:   Wearing a seatbelt is not just a good idea it's the law.Even if one or both of the fused sentences contain internal punctuation, the sentence is still run-on.
A comma splice is the unjustifiable use of only a comma to combine two separate sentences. (One should use either a period, a semicolon, or a coordinating conjunction and a comma to separate the two statements.)
Comma splice:  Wearing a seatbelt is not just a good idea, it's the law.Both run-on sentences and comma splices may be corrected in any of the following ways:
Run-on:            Tevon won the award he had the highest score.If a conjunctive adverb like therefore, however, then, or consequently separates the two sentences, use a semicolon also.
A fragment is an incomplete construction which may or may not have a subject and a verb. Specifically, a fragment is a group of words pretending to be a sentence.
Fragment:   Traffic was stalled for ten miles on the freeway. Because repairs were being made on potholes.
Revision:     Traffic was stalled for ten miles on the freeway because repairs were being made on potholes.
Fragment:   It was an excellent movie; one that was nominated for an Oscar.
Fragment:   It was an excellent movie. One that was nominated for an Oscar.
Revision:     It was an excellent movie, one that was nominated for an Oscar.
Fragment:   Prospectors invaded the newly discovered territory. Some in wagons, some on horseback, and a few in heavily laden canoes.
Fragment:   Prospectors invaded the newly discovered territory; some in wagons, some on horseback, and a few in heavily laden canoes.
Revision:     Prospectors invaded the newly discovered territory, some in wagons, some on horseback, and a few in heavily laden canoes.
