In literary terms, the word “Series” can describe a set of stories that take place sequentially, it can be used to describe a set of stories set in the same world (q.v.) but that are totally unrelated, it can be used to describe a set of related stories that are not serial but do use the same characters, and so on. That kind of imprecision is all fine and good when writing a stand alone article, but when writing a descriptive review, it doesn’t really tell the reader much. To that end, I’ve decided to come up with a set of terms that further define stories and put them into a better context.
The terms used on this site are a series of subcategories that are primarily inclusive and not necessarily exclusive. Thus, a story that is defined as part of a Series could be a World, a Serial, a Cycle and a Saga (q.v.). Note, however, a while a story could be both a Stand Alone Novel and part of a Series, it cannot be Consecutive Serial (q.v.) and a Stand Alone Novel. This will hopefully all become clear once the definitions are outline below.
Stand Alone Novel: This is a book that stands on its own. It has its own beginning, middle and end and can be read independently of other stories. Such a book could, however, be part of a Series (q.v.), as long as one need not know anything about the other books in that Series to enjoy it. Most books out there are stand alone novels, and most stand totally on their own without being part of a series.
Some Stand Alone Novels that are also parts of Series include: John LeCarré’s Tinker, Tailor, Soldier, Spy, Alistair Reynold’s The Prefect and Chasm City, all of Iain M. Banks‘ Culture novels, J.R.R. Tolkien‘s The Hobbit (but NOT The Lord of the Rings) and many others.
Series: Any collection of stories that are related through a set of shared characters, settings or plot lines. Any book that has any sequel, prequel or continuation is part of a series. I could also stand alone.
World: A setting created by an author that describes an existence that is in some way different from our own. That difference could be due to temporal setting (far future, distant past), alternate reality (with different laws of physics, existence of magic or the like), alternate timeline (where some event has changed the course of history), or any similar created element that clearly sets the story in an extraordinary existence.
A World does NOT include stories that are supposed to be happening in our universe and follow generally accepted laws of reality. Thus, the Sookie Stackhouse Stories can be considered a World because while they take place on a modern day earth, they include rules of existence that don’t match the generally excepted view of reality (i.e. vampires exist). In contrast, The Inspector O series are not considered a Series World because they are supposed to be set in the modern world and there is no alternate magic, science or the like.
Examples of Series World: J.R.R. Tolkien’s Middle Earth (which includes the Hobbit, the Lord of the Rings, The Silmarillion and others), Iain M. Banks’ Culture universe, Alistair Reynold’s Revelation Space universe, Kat Richardson’s Grey Walker Series, Ursula K. LeGuin‘s Hainish cycle, Robert Harris’ Fatherland, the Eric Flint (et al’s) 1632 series, etc.
Chronicle: A set of stories that follow a given sequence of events in the tales, but in which each story may have its own beginning, middle and end. This subcategory includes most books one thinks of as a Series.
Examples: James Church’s Inspector O novels, John LeCarré’s George Smiley stories, Frank Herbert’s Dune novels, and Ursula K. LeGuine’s Earth Sea stories are all examples of a Chronicle. Alistair Reynold’s has several books that are a serial within his Revelation Space Novels: Revelation Space (2000), Redemption Ark (2002) and Absolution Gap (2003), but notably these do not include Chasm City (2001), Diamond Dogs, Turquoise Days (2003), Galactic North (2006) or The Prefect (2007), which are part of the same World and the same Cycle, but not part of the above Chronicle.
Trilogy: A Chronicle that is broken into three parts. These can be stand alone novels, but are most frequently Serials.
Examples: J.R.R. Tolkien’s The Lord of the Rings, Alistair Reynolds’ Revelation Space, Redemption Ark, and Absolution Gap (but not the other stories set in the Revelation Space World or Saga (q.v.)).
Serial: A subset of the Chronicle that includes on going stories that must be read in a given sequence and do not end at the conclusion of any one volume. Most Trilogies and many other books fall into this category. In that sense, they are in fact a single story that needs multiple volumes to tell it.
Examples: J.R.R. Tolkien’s The Lord of the Rings (but NOT The Hobbit or The Silmarillion (q.v.)), George R. R. Martin’s The Game of Thrones, and Dan Simmons’ Hyperion Cantos. 
Saga: Stories that follow the same characters, plots or directly related series of events through a set of stories that are related and tell an on going tale, but have definitive conclusions along the way. They may (or may not) include Serials as part of the Saga. The best example would be J.R.R. Tolkien’s The Hobbit and The Lord of the Ring; The Hobbit is a stand alone story that starts the Saga of Sauron’s Ring, which is then concluded in the Consecutive Serial: The Lord of the Rings.
Examples of Sagas: James’ Church’s Inspector O Novels, C.S. Forrester’s Horatio Hornblower tales, David Webber’s Honor Harrington Series (for the most part anyway), John LeCarré’s George Smiley Stories, including Call for the Dead, The Spy Who Came in From the Cold, A Murder of Quality, The Looking Glass War, and the Karla Trilogy (a Serial, but not a Consecutive Serial since all three stories can be read alone), The Secret Pilgrim, and many other of his books that share some of the same characters across their pages.
Perhaps the best example of a Saga is The Drizzt Do Urden’s tales by R.A. Salvatore. These are a Saga made up of a set of Consecutive Serials, most of them being (trilogies).
Cycle: Set of stories that chronicle a set of related tales, sagas or the like, but include independent stories or series that have their own beginning, ends and middles. When viewed on a large canvas, however, they relate interrelated stories that tell a larger tale.
For example, the Stand Alone Novel The Hobbit and the Consecutive Serial The Lord of the Rings are part of a Saga telling about hobbits and their relationship to Sauron’s Ring of Power. The Silmarillion is a book that tells a set of stories that take place in the same World (Middle Earth), share some characters, and tell of related events, but do not actually tell a continuous story line.
Examples: Alistair Reynolds’ books Chasm City (2001), Diamond Dogs, Turquoise Days (2003), and Galactic North (2006) are not only set in the same World as the Revelation Space Trilogy/Chronicle, but also tell stories that are related in some way to the events that occur within it. His book The Prefect, however, is arguably not be part of that cycle, though it is set in the same World and shares certain historic setting events. Similarly, many of John LeCarré’s novels are part of the same Cycle, as is revealed in the Secret Pilgrim which ties many of his classic Cold War Smiley tales together with his subsequent Post-Cold War novels.
I’m sure I could (and probably will) go on beyond that, but for now, this seems a good place to start. Again, comments and ideas are welcome. Like any good Seriation, this is a work in progress.