Business requirements and functional requirements have different purposes and are used by different parties on a software project:
Business requirements have a purpose to capture end-user needs, i.e., they should be statements about WHAT an application should do for the end-user. Business requirements are first used by project management to plan the next release:
a) agree with the end-users on the release scope;
b) estimate the development effort;
After the release scope has been agreed, business requirements are used by BA (or developers) to specify solutions to the needs. These solutions (i.e. HOW TO details) are captured as software requirements (where functional requirements are a kind of software requirements). Functional requirements are used by developers and testers.
To summarize, business requirements should capture WHAT an application should do, whereas functional requirements should capture HOW the user needs can be implemented (from the end-user perspective).
Hope, this could help. Yuri