The key difference between sentence fragment and run on is that a sentence fragment is a string of words that cannot form a complete thought on its own while a run on sentence is a sentence that is missing the right punctuation to make the sentence flow properly.
Sentence fragments and run on sentences are two of the most common errors most of us make in our writing. A complete sentence has three main elements: a subject, a predicate and a complete thought (ability to stand alone). Recognizing these elements is the first step in learning to identify sentence fragments and run-on sentences.