A simple sentence is a whole sentence. A sentence fragment isn’t. A run-on sentence is not necessarily long.

In its simplest form, a sentence consists of a subject and a predicate.

Simple sentence: She fainted.

Sentence fragment: Because she fainted.

The addition of a subordinate conjunction—because, in this case—makes a simple sentence into a subordinate clause.

Run-on sentence: She fainted, he saw her lying there and thought she was dead.

A run-on sentence is not a long and complicated sentence. It is two or more sentences punctuated as one.

In the “She fainted” example above, start a new sentence with "He saw," or change the comma after “fainted” to a semicolon. The misuse of a comma in this sentence is called a comma splice, or comma fault.

Some writers use sentence fragments, comma faults and other “incorrect” forms deliberately, and they do it well.

From “Voices” by David Albahari, in Geist 64:

My friend and I exchange glances. Problems with writers? In a bar, perhaps, but in a coffee place?

From “Fiver” by Stephen Smith, in Geist #63:

It was right there, between the seats, in the drinks holder. Someone’s bottle of water beside it. A pen. They had a dashboard compass. North, it said.

If you’re going to break the rules, get a good grip on them first.