Use Cases are goals of the software. So by
placing the word “business” in front of them it sounds like we are talking about goals of the business.

A use case is a diagrammatic representation of functional requirements. It is used to capture the actions which a system should take while performing a business process. For example Online banking, system should ask the user to login with the userid and the password. Now for a particular bank the business rule here could be that the user should answer the secret question before allowed to be loggen in. Once the user is logged in then he is navigated to the accounts page where user can perform various actions depending upon the usr requirement. So this functionality could be captured using the Use Cases showing the interaction of the system and the user. This simple to understand representation is very helpful to make the stakeholders and also the developers understand that how a particular module or a functionality works.

A use case in software engineering and systems engineering is a description of a system’s behavior as it responds to a request that originates from outside of that system. In other words, a use case describes "who" can do "what" with the system in question. The use case technique is used to capture a system's behavioral requirements by detailing scenario-driven threads through the functional requirements.
Each use case focuses on describing how to achieve a goal or a task."

A use case should:
• Describe what the system shall do for the actor to achieve a particular goal.
• Include no implementation-specific language.
• Be at the appropriate level of detail.
• Not include detail regarding user interfaces and screens. This is done in user-interface design, which references the use case and its business rules
A use case (or set of use cases) has these characteristics:
• Organizes functional requirements
• Models the goals of system/actor (user) interactions
• Records paths (called scenarios) from trigger events to goals
• Describes one main flow of events (also called a basic course of action), and possibly other ones, called exceptional flows of events (also called alternate courses of action)
• Is multi-level, so that one use case can use the functionality of another one.

Use case or use case narrative meaning is same?