The course stream is a general dialogue space where students post comments and upload files (audio, photos, video). All of these activities are viewable in the stream feed, similar to the layout of a Facebook wall.
A discussion board, on the other hand, is a conversation thread that is typically implemented in a lesson. Unlike the course stream, a discussion does not have all of the same multimedia capabilities. Instead, it acts as a conversation thread where students can post and respond to each others’ comments related to a particular lesson.