Team Coach - The Agile equivalent of a certified ScrumMaster. The only reason the "coach" term applies here is because it harkens back to when XP called its ScrumMaster equivalent position an "XP coach." I prefer to call it a "team facilitator" if the team is not using Scrum. This person typically facilitates one team, and maybe two teams in a rare circumstance. Usually this person will have the equivalent of a CSM or PSM I certification. This person generally interfaces with front line managers and team leads(if they exist, some Agile orgs don't have these front line managers and/or team leads) to coach them on how best to take advantage of Agile. Hopefully the Team Coach will report to a Teams Coach if there are more than a few teams at the org.

Teams Coach - A coach who coaches ~2-7 "Team Coaches" and by extension, their teams. Usually this person will have the equivalent of a CSP or PSM II certification. This person generally interfaces with senior managers and directors to coach them on how best to take advantage of Agile. This person, at times, may also play the role of "Team Coach" for a team that is just starting up or needs significant help. Hopefully the Teams Coach will report to an Organizational Coach if the org is large enough.

Organizational Coach - This person generally oversees 8 or more Teams or 3 or more Team Coaches(and by extension, their teams), or is the coach for the entire organization altogether. This person generally interfaces with executives and upper management to coach them on how best to take advantage of Agile. A Certified Scrum Coach is an example of this type of coach, but there are only ~50 CSC's in the world, though there are probably another 50 or more in the world who are of roughly the same skill level and experience but don't have the cert.

Other Agile Coaching Classifications
These classifications are pretty analogous to the Agile Coaching levels described by the International Consortium for Agile.

See "Types of Agile Coaches" (you have to scroll down a bit) here: