Actually, there is a third situation to use a semicolon. When you have a compound sentence composed of two rather long sentences, you may use a semicolon and a coordinating conjunction instead of a comma and a conjunction in order to more thoroughly separate the sentences.
Philip, I agree. But that’s not a third way; that’s the complete thoughts point. It was just semantics in the explanation… a complete sentence must be made from a complete thought containing a subject (sometimes implied) and a predicate. So the joining you described is exactly the joining I described as my second scenario.
stuart, you wouldn’t divide a list with semicolons unless the individual list items themselves contained commas. Period.
(see what I did there? Hee hee)
Owngry, the colon is used mainly to introduce either a thought or a list.
“I will tell you this: I love to yoyo.”
“Obtain the following: a yoyo, a polyester string, and a nice dry bearing.”