In a compilation, contributors add relatively independent items to a collection. Our class roster is a simple example -- each of us added our name and email address. We all followed the same format and added the same information, but each had our own, independent entries. Other examples include collections of reviews of books, Web sites, or movies. One generally creates and edits their portion of the evolving document, but does not make major changes to other's entries.
With a co-authored document, the division of labor is less clear. One person may begin with an outline and invite others to flesh the content out. Another possibility is that one person will write a first draft, then invite others to modify it. Wikipedia articles are a well known examples of jointly authored documents. In either case, all authors are free to edit any portion of the evolving document.
There is a gray area between these -- one person may revise someone else's contribution to a compilation. One thing all wikis have in common: when you visit a wiki, you should try to improve it.