The PM keeps lists of stuff, goes to meetings, and ask people when they'll be done. A good PM is a combination of a guy that wears a bow tie and pocket protector, and a mob enforcer - meticulous, but feared.
The BSA comes in after the senior management has decided what to do, tries to figure out what they agreed on and writes it all down. Then he figures out what actual work needs to be done by talking with the actual system users and the IT staff and writes that all down. Finally, he works all that information into some sort of document.
The best analyst I ever hired was an English major who could read anything and summarize it concisely without actually knowing anything about the subject. Some basic familiarity with subject area knowledge is useful but not really required if you can read and think. In fact knowledge may be a hindrance if it causes you to become invested in one solution over another. You are not the business owner or the system designer - you are there to document the requirements.
The resulting document is used as the basis of an agreement between the business (who is paying for the work) and the IT department (who will be responsible for getting the work done), and will be used later to assess blame.
The BSA may or may not be involved with writing the technical spec with the IT staff and developers. Developers are however, usually quite willing to off-load this task to someone who can write in English.
As the IT staff deliver components the BSA may also be involved in writing the acceptance tests and working with the QA team to run the tests and present results.
You probably will not need to write any code but you will need to be a user of everything. Every application on every system, every database and file system, every messaging system, and every script on every network. You will also need keep track of the business owners, actual system users, operations support team and developers involved. It is very important that you know how to get developer level access to all this and keep track of all the who/what/where through all of the changes.
Note: If you are not given the authority to fire anyone you work with (and even then); nothing anyone tells you is true unless you can verify it yourself - so database, scripting and coding skills are very useful.