The IT-hype cycle adds the word 'business' as a modifier to many words representing IT-related artifacts like process, application, requirement, service, and … rule.  The meaning of the artifact itself hardly changes when adding this modifier; instead, this modifier is used to indicate that the concept is 'important to the business'.  Now, the issue with 'business rule' is that the presentation form of a 'rule for IT' and a 'rule for the business' is very different.  The two examples below indicate the different presentation forms.

Business rule (based on SBVR-RuleSpeak):

A discount of 15% must be applied on the shopping cart if the shopping cart contains between 2 and 4 items and one of the following conditions are met:
    -  the purchase value is greater than $100 and
          the customer category is gold
    -  the purchase value is greater than $200 and
          the customer category is silver

IT rule (based on PRR-OCL):

Rule discount
ruleVariable:
  ?customer: Customer = Customer->any()
  ?shoppingCart: ShoppingCart = ShoppingCart->any(c: customer | c=?customer)
Condition:
  (?shoppingCart.containsItemsInRange(2, 4)
  and
    (((?shoppingCart.items->collect(i:Item|i.value))->sum()>100 and    
      ?customer.category == "Gold")
    or ((?shoppingCart.items->collect(value))->sum() > 200 and
      ?customer.category == "Silver")))
Action:
shoppingCart.discountValue = shoppingCart.discountValue+15

The meaning of the word 'business rule', following the previously-described trend of adding the word 'business' as modifier to IT-related artifacts, is often misunderstood as 'an IT rule that is important to the business'.  Instead, it should be 'a rule that under business jurisdiction'.  Unfortunately, the former notion seems to be prevailing in the market that is dominated by IT-related tool and service providers.

The efforts of the Business Rules Group, the SBVR team, and Ron Ross have disambiguated the word 'rule' in recent years.  The now prevailing definition
   "is a statement that defines or constrains some aspect of the business"
works very well and I don't believe there is much discussion any more on this topic.

The word 'management' was thought to be unambiguous — 'management' being defined as the whole process of creation, updating, making available for others to use, and explore.  However, again due to a prevailing IT-dominated perspective, it has been reduced in one of Gartner's reports (Business Rules Management:  State of the Art  ESC19_811,11/07, AE) to mean the management of rules through the application life cycle.