Three forms of Trilogy

The trilogy (or any group of stories) (specifaclly Sci-Fi and Fantasy) has three forms.
The first, and most popular, is that of a large tale told in three stories. The characters do not change a lot between the books but the plot is signicantly different, though an overlying plot will tie them all together. As stories the later ones can stand alone, though they gain much more from being read together. The first four books of Harry Potter are of this type.
The second most common type is that of the non-unified tale. These stories sometimes involve the same main characters but something has changed them as a person greatly. This also includes any set of tales located in the same world with different major characters, though they are usually in some way related. The Star Wars books are a good example of this kind.
The final type of collection is the single volume. These are essentiually a single story broken into multiple volumes (usually three). Unlike in the others, the sub-plots take less attention than does the major plot and there is little change in time between volumes. This is by far the most complicated version, because it requires the entire story to essentially be laid out by the publication of the first book. The Lord of the Rings is the best example of this type.