There are less than 50 Certified Church Consultants in the United States! Be sure you are working with a qualified consultant like myself.
The key is that a consultant "tells" the client what to do. Usually a consultant is hired as the "expert," does an assessment and then makes recommendations as to what needs to be done.
While a consultant will tell people what to do, a coach will assist people in discovering within themselves what needs to be done.
This normally deals with the inner feelings, the mental health, experiences of the past and the "insight" needed to make changes. The focus is on the past - healing - resolving.
Coaching focuses more on the future and is all about discovery - action & achievement - being proactive & creative.
Often this process is used in the church/ministry setting so that a "more experienced" person can share with and help a "less experienced" person in the life and ministry issues that are faced. Mentors share what they did, and this process is about transfering knowledge.
A coach may or may not have experience in a certain area, but they are able to focus on and draw out the person's successes and learnings. Coaches walk with you as you discover how best you will do ministry.
Each of these professions is very helpful and many leaders employ some or all of them throughout their careers. The important this for you is to understand the differences and to engage with the correct one at this time in your ministry.