What's the difference between a Scrum Master and a Senior Scrum Master?

What's the difference between a Scrum Master and a Senior Scrum Master?

One word. 

From the "doing a job" perspective I really don't see a difference between someone that is starting to fulfill the Scrum Master responsibility and one that has done it before.  However, since the Scrum framework has job responsibilities and not job descriptions, it would be up to the organization that insists on having job classifications to define.  This is one of those things that the Scrum framework leaves up to the organization.

 the description is a confusing list of expectations mixed between managing other Scrum Masters to reporting to management.

That sounds against the concept of self-management, self-organization.  But it also informs me that your organization uses a hierarchical leveling scheme, that there is an expectation for managers and individual efforts are valued/rewarded more than a team's.  I've said this before.  Scrum assumes a servant-leader environment that allows decisions to be made closest to the work.  But, at least in the United States, that kind of organization is extremely rare.  The Scrum purist in me would like to say that any organization can transform itself to that methodology, but the Business realist in me knows that isn't true. 

It comes down to why the company needs to have this internal position.

One common reason is pay bands. To have different pay bands, the company may need different titles. Therefore, you see levels (I, II, III) or prefixes (junior, senior, principal). In this case, the role should require demonstrating a greater level of expertise and experience over the previous level. It may or may not have anything to do with management of others, but I could see that being valuable.

I would suggest that there be a clear roadmap for career progression within a role that considers both growing competency in a topic (for Scrum Masters, the Scrum framework, lean, and agility) as well as moving into a people management role, and having alignment that shows career progression.

What's the difference between a Scrum Master and a Senior Scrum Master?

Quite possibly the difference between a Scrum initiative succeeding or failing. Organizations love their hierarchies, even to the point of trying to impose them on Scrum accountabilities. What are the chances of success when you have that sort of organizational gravity to overcome?