BUSINESS PROCESS
Within your application, business processes are the logic of it. That is, how the flow works within your application, here it would define the structure of your application. How do the different components of your application interact until they complete the flow?
FUNCTIONAL DESCRIPTION
Operation of the application at the functional level, that is, we abstract from the internal logic of the application and explain it at the operating level. This part should not be technical since the client should be able to understand it perfectly. Here I would put the documents of use cases, uml diagrams if necessary ...
As a tip for functional description I would try to follow the pattern of use cases, as a user I have to be able to do ... (substitute user for the actor of your use case and ellipses for the logic that makes the application).
I hope I have helped you.