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. However, a special team 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 business. For example, a consultant might tell you how to eliminate waste in a manufacturing process or design your website. Other consultants are generalists working on a range of issues. Still, again there is a specific deliverable in mind, a report, or a recommendation to make a specific change or set of business changes. 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 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 be self-sufficient so that the staff can solve issues independently and become capable of sustaining that improved performance.