As far as the end-user is concerned, the difference between a wiki and a blog is that in a blog, each post by a contributor is kept separate.  Access could be set so multiple users could edit a post, but there is no mechanism for tracking the changes.

In a wiki each collabotator is tracked as to what is modified.  Difference and comparisons in versions can easily be inspected with the final product being a single document.

There are several disciplines requiring student collaboration where a wiki could be seamlessly integrated into a course.  The first is the lab sciences.  There students work as teams and often produce one laboratory report.  The wiki a natural medium for the collaborative report.  The instructor could easily identify the student contributions, which student is taking the lead in editing and such.

The second area is in computer courses.  A wiki is a perfect tool where software engineering can be implemented.  Several student programmers could use a wiki to implement a program far greater than any one student could.  For years, I have taught such courses and implement software engineering protocols.  In the spring of 07, I plan on using a wiki to develop code in two classes, CMP 220: Analysis of Computer Archetecture and Software  and CMP 217: The C Programming Language so stay tuned.