role of a consultant

Organizational and leadership experts can perform at least two different roles. One is the role of a consultant. The other is the role of a coach. What is similar about a consultant and a coach and the process that each uses? What is different? Can the same person perform both? Can the same person perform both in the same organization? Are there other similar roles (e.g., counselor, advisor, mentor, etc.)? How do those roles compare/contrast to the coaching role? Leadership lessons you can learn?