The main difference between coaching and consulting is that coaching pulls out answers from the client while consulting tells the client what to do.
A consultant is usually an SME, a subject matter expert who can provide technical and professional advice to clients based on their situation. A coach, however, helps clients find their own clarity and answers, and helps them to understand how to move forward in achieving their goals and grow personally.
When you coach, you explore possibilities. When you consult, you provide possibilities.