No. While a business coach definitely does some consulting, a consultant does not coach.
A pure consultant is basically a specialist dealing with a certain area of a business. For example, a consultant might be able to tell you how to eliminate waste in a manufacturing process. Typically, a consultant is project/problem specific, and details his findings in a report.
A coach doesn't concentrate on a single area, doesn't necessarily prepare formal reports, doesn't concentrate on ONLY the business, and doesn't leave once a specific project is completed. A coach is there for you - 24 hours a day - to help you, guide you, motivate you, improve you, and improve your entire business.