A forum is a place for open discussions, where you post questions or comments and other members join in adding comments and questions to what you have posted, like an online discussion group.
A blog is a place where you put out articles or a virtual diary of thoughts or ideas. While people can and do place comments after a blog, it does not evolve into a long threaded discussion group.
They are similar and it can get confusing sometimes. I use my blog to post stories about my searches and discoveries of my family history, memories of those family members who have passed way. I know that others have used their blogs in a similar fashion or to publish articles about other genealogy related areas or even how to help tips. I use the forums to put out information that will help other members or to ask questions of other members that might be researching in the same areas I am or to touch base with people that have similar interests as myself.