The key difference between a rule and a constraint
A rule is something which will advance your purpose. A rule that you need to swipe in before you enter the building ensures only valid people come in your building. A rule that you should perform A before B so that the outcome C is always optimum. These are the rules which advance your purpose.
On the other hand constraint is a limiting factor in your system (not just IT systems). System is your ecosystem. Only 5 people can swipe for entering in the building at the same time. Perform A before B as there is no other way to achieve your outcome C.
Constraint can be interpreted as a rule if you change your perception! Hence, sometimes they are used interchangeably.
The difference between the two is that the former says: “we must have this” and the latter says “we are prevented from doing something because of xxxxx constraint”. There are many other types of constraints, such as technology (both hardware and software), cost (human resource costs and licence fees) and time (project must be delivered by March because of legislation or after May because of scheduling conflicts).
Here's a more concrete (but simplified) example:
Business Need: the mobile application must be supported by iPhones.
Business Constraint: our software we use to create the mobile application only supports iPhone 6 and up.
Key Takeaway
A business rule 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.