I do believe there is a difference there, however. A brand is what people perceive of you before they know anything about your reputation. What do they see around the web? What image do you put off when you walk in the room? How do you treat people? What do your correspondence cards look like? How do you communicate? Those are all elements of a brand.
A reputation is all about what other people have to say and how you are preceded by what those people say. That includes things like LinkedIn recommendations, hearsay, references, etc.
Thoughts? What other terms would you use to describe the two different aspects? I do think it's important to distinguish.