Use Case : It is way Business requirements are presented. BSR is where the use cases are written.
For example :
Case1 : User will login as normal login
Result: Message "Welcome normal user" is displayed
Case 2: User will login as admin user
Result: Message "Welcome admin user"
Case: Admin when clicks on properties will have access to create users
Result: Admin user can change the rights
FSR: It will be more detailed functional knowledge of the system.
SRS: This is the document that the organisation would write who is developing the system according to their understanding for FSR and BSR.
To be frank, there is only one or 2 documents that a company would follow and these terms are often interchanged.
I dont knw what FSD is . Did you mean Functional Design Spec.
Usecase: It is a document which it will explain about the input conditions,business logic and the output conditions.
SRS : It is a system requirement specification document which will define the software,hardware requirements which you have to be used in the project.
FRS : It is a functional requirement speicificaion doucument which will define the exact functionality of particular module/project.
BRS : Business requirement specification: This is the document where the exact business requirement will be noted.
This document is prepared after completion of the information gathering from the client mainly based on BRS [Business Requirement Specification] will analyze the requirements and develops a new system and functional requirements specification to be developed as a new software.
Use Case: In this document the Use Case description and the task flow diagrams are prepared for the overall application based on the requirements specified by the BRS. Use cases are included in the SRS document only so both equal.