Brand Identity is not just logos and business cards, but I'll concede that is a lot of it. Branding includes all aspects of your company with which people visually interact. That means more than just a stationery package consisting of a business card, letterhead, and envelopes. That includes things like interior and exterior signage, packaging, labeling, even stuff like fax sheets and word processing templates.
And, you'll notice that I said "people" not "customers": having a well-designed and unified brand builds not only your public esteem and recognition, but also employee satisfaction and loyalty. Think about why companies like Apple have such a carefully and thoughtfully designed corporate image.
I have known fantastic graphic designers that couldn't design a logo to save a schoolbus full of children. I also know an amazing logo designer who would not design and produce a magazine, even if you held a gun to his head. They are very different skill sets, requiring very different creative processes. I feel very fortunate that I have significant skills in both areas.