Jay,

You may feel confused but I think you are probably closer to understanding this role than you think based on your post.  Business Change Analyst, Change Analyst, Change Management, are all related.  Of course, what is expected of you typically depends on the organization since all organizations have their own flavor of common roles.  

Consider the case where a Business Change Analyst (typically a specialization of the Business Analyst) is working on a project team that is implementing a new system or process.  The team has analyzed the As-Is state of things and determined the desired To-Be state.  They are creating a new system or process to support that To-Be state.  However, just replacing a system or process overnight could create chaos for the business workers/employees and clients of the company.  The Business Change Analyst is charged with identifying problems and disruptions that may occur while migrating from the As-Is state to the To-Be state (from point A to B). Then figuring out how the transition must occur to avoid such disruptions.

With a new system:

• Employees will require training on the new system
• Employees will need to know if they use the new or old system in specific cases for some transition period
• Clients may need to be transition incrementally to the new system
• Other areas of the organization may need to be coordinated with to ensure transition to the new system occurs smoothly

Just to name a few.  And many of these can apply to new processes as well.

Basically, anything that should be considered and managed to get the organization smoothly from point A to B falls within the space of the Business Change Analyst.  It should be noted that Business Change Analyst can also be used on project where the company is anticipating a change in strategy.  What will need to be considered to move from direction A to direction B.

Hope this helps.