To my way of thinking, a beta reader does whatever he/she and the writer agree the beta will do. Some betas edit and proof read. Others don't. Some betas give comments on the most minute details, while others are strictly big picture commentators. I typically have two sets of betas. The first set to read an earlier draft and point out glaring problems with the plot, character development, and the story's premise. Many drafts later, after the big problems have been solved and the book is much more polished, I have another set of beta readers to look at more subtle elements such as style and narrative tone.
Basically, you take what you're looking for out of a reader and try to mesh up with what any given reader is willing to provide you. That's what a beta reader does.