Now that I've created a Wiki and a Blog, I see a few difference between them.
Blog's have very much a single direction. I post updates to them for people to read. While people can make comments, their input is not as significant as my initial posts.
Wiki's are very bi-directional and collaborative. Regardless of who creates an entry, everyone is treated as an equal. in fact everyone is expected to add input equally.
How would I use Blogs and Wikis?
I would use a blog to post information, notes, link, and videos to my students. If they have a question, they could make a comment. But notice the blog is very teacher centered.
I would set up a wiki for teams of students to talk to each other. It allows them to collaborate and learn together.