Business rule vs. functional requirement

I'm taking a course in business analysis, and thought that requirements gathering would be the easy part for me, since I have been documenting and reading requirements before, but now I realize I really don't really get the difference between  a functional requirement and a business rule.

Wikipedia: "a functional requirement defines a function of a software system or its component. A function is described as a set of inputs, the behavior, and outputs. Functional requirements may be calculations, technical details, data manipulation and processing and other specific functionality that define what a system is supposed to accomplish. Behavioral requirements describing all the cases where the system uses the functional requirements are captured in use cases." 

BABOK defines functional requirements as "the product capabilities, or things the product must do for its users."

Wikipedia: "A business rule is a rule of a business, company, or corporation. It is a rule that defines or constrains some aspect of business and always resolves to either true or false. Business rules are intended to assert business structure or to control or influence the behavior of the business. Business rules describe the operations, definitions and constraints that apply to an organization. Business rules can apply to people, processes, corporate behavior and computing systems in an organization, and are put in place to help the organization achieve its goals."

The course material describes business rules as obligations concerning actions, processes, and procedures that define, and possibly constrain, some aspect of the business. 

Ok, now it's starting to make sense to me, this is my conclusion:
- Functional requirements often start with "the system shall.." or "the system must..", as they state what the system must be capable of doing,

 - Business rules simply state what rules must be followed,  by the people, processes or systems.