A "briefing" is a term from advertising & PR agencies. It is a document in which the customer explains what their business context, goals and "value demand" is, at what budget etc etc.

Thanks for the link, I will look into it. I worked with use cases and user stories, but user stories will frequently have some gaps in them - and it's in those gaps that misunderstandings occur. I was hoping that there's a universal language to create bullet proof models.

"create bullet proof models"

Assuming that is possible (for anything but the most simplistic of systems) is likely the root of your problem.

I thought this might be ambitious, yes. Although at this time the system is (still) really quite simple.

Also, I thought: there must be a better way than saying: "So when user A logs in and merges records X and Y, user B will see the changes but not user C because he's not an admin".

But apparently I am mistaken?

I'd wager you just aren't being clear enough. From what you just said, I have zero context as to why user B can see those changes. I can make a guess, because he's an admin, but it's just that, a guess based on the little context you provided about user C not being an admin and being unable to see the changes.