Basically I view all the types of collaborative stories the same way.  It's a group effort.  There are many different ways of handling it but basically I think we need to allow some freedom and flexibility in story tag efforts and not be too rigid.  But for informational purposes I post the following. 

Definitions

Story Circle
One person begins a tale and stops after a few sentences. The next person picks up the story thread and continues it, then stops. Next person adds to it and so on until the tale comes to a resolution. The story could begin with a pre-selected title or subject to guide the improvisation. Try recording the story circle on a tape recorder for later listening.
http://www.storyarts.org/lessonplans/lessonideas/#circle

Chain Story:
-Everybody knows what a chain story is, right? If you want to participate, please add one sentence to the previous sentence. Alternating, at least, one other person would need to add a line before you could add your next sentence.
-A chain story is a story written bit by bit, by many different people.
-Each person takes a turn moving the story along and each new person who takes over must maintain some consistency in the narrative while being free to take the story in other directions.

Story Tag
Story Tag is a multi-author, round robin type of cartoon. One person starts it, another person continues, and the cartoon keeps going until someone ends it
 Story Tag 1
Story Tag is a multi-author, round robin type of cartoon. One person starts it, ... Story Tag 01 is the product of two authors: Gel and Dustball. So is Tag. ...
http://www.newgrounds.com/portal/view/98457 -

Round Robin
A round-robin story is one that is started by one person and then continued sucessively by others in turn. Whether an author can get additional turns, how many lines each person can contribute, and how the story can be ended depend on the rules. Some Web sites have been created for the telling of round robin stories by each person posting the next part of the story as part of an online conference thread.
A Round-robin story, or simply "round robin," is a type of collaborative fiction or storytelling in which a number of authors each write chapters of a novel or pieces of a story, in rounds. Round-robin novels were invented in the 19th century, and later became a tradition particularly in science fiction. In modern usage, the term often applies to collaborative fan fiction, particularly on the Internet, though it can also refer to friends or family telling stories at a sleepover, around a campfire, etc.

http://en.wikipedia.org/wiki/Round-robin_story

I found these definitions on a number of web sites.  It was a hard thing to find much information on and I was surprised.  If anyone has an "official" definition I can post on the web site, that would be great.  PM me. ;)