As of now, you got quite a good idea over what are the roles and responsibilities of the business analyst. A business analyst looks at all the business processes end to end. He analyzes and also suggests the changes in the business processes if needed. That is where his work differentiates from the project manager. A Project manager understands the requirement and creates a project plan like how many resources are required to complete the task?, What tools are required to complete the task? How much time it will take to complete the project? Assigning resources like developers, testers, etc.
Where in the job of the business analysts to manage the whole team including project managers. The business analyst gives the project details to the business analyst. He is the one who knows the business processes and its functionality. He focuses more on the end products. He addresses all the team members, customers, and stakeholders.
Project managers are the internal role and he obtains a team to perform a task efficiently. He is more closely work with the developers and testers. His role is managing the project from understanding requirements- designing- coding- testing and the implementation in the project life cycle. On top of that, he must have the strong technical knowledge and ability to monitor and mitigate the risks in the project parallelly.
However, due to the financial constraints, these two roles are performed by one person in a few organizations. But there is a possibility of poor quality of work as a lot of work has to manage.