No. While a business coach definitely does some consulting, a consultant generally does not coach. To use a sports analogy, a football coach never touches the ball during a game; the coach helps the players to do their best. A special team however, is like a consultant; they are called in to perform a specific task during the game and are actually on the field.
Typically, a consultant is project/problem specific, and details findings in a report. Some consultants are specialists 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 or design your website. Other consultants are generalists working on a range of issues, but again there is a specific deliverable in mind, a report or a recommendation to make a specific change or set of changes to a business. The consultant generally leaves behind a report that the client then implements on their own. Consultants are specifically valuable to a company when they need a certain expertise for a short period of time and where it is not economically justified or even feasible to maintain this level of expertise in house.
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, your effectiveness, and improve your entire business. The coach's primary goal is capability building, helping the business to be self sufficient, so that the staff can solve issues on their own and to become capable of sustaining that improved performance.