1. Sentence fragment.  It begins with a capital letter and ends with a period.  But don't be fooled.  The fragment doesn't express a meaningful idea.  Fragments most commonly occur when writers put a period where a comma is required.  There is such a thing as the intentional fragment.  Short, emphatic sentences.  Use them sparingly.  And when you lay down an intentional fragment, do it on purpose. 
     
2. Comma splice.  The fragment occurs when a period is used instead of a comma.  The comma splice is the reverse: a comma is used where there should be a period.  Student writers equate short sentences with bad style, and they string one sentence after another together with commas.  Bad idea.  Pay attention.  Remember these words: period at the end of sentence.  Words to live by.
       
3. Run On.  No comma, no period. Nothing.  The run on is two sentences that need a period in the worst way.  Not a comma.  Words to live by?  They apply here, too.