Sentence Fragment: a group of words that does NOT tell a complete thought. A fragment is missing a subject, a predicate, or sometimes both.
ex. Went to the movies. [missing a subject]
ex. My brother and sister. [missing a predicate]
Run-On Sentence: has two complete thoughts, or sentences, that run into each other. The end punctuation of the first sentence is missing, and the second sentence is often missing a capital letter.
ex. Georgianna enjoys mysteries he reads a new one each week.