Requirements or Model: how to write the statements

There is an idea that systems should at first be described as a black box, and requirements engineering is devoted to ways of such description. Goal: if we check the system for compliance with the requirements, we guarantee that the system is adequate for business needs. But it doesn't work that way. So, it makes no sense to go too deep into the requirements, but you should quickly start to make models or use easy formats for requirements. 

I'll review different approaches to writing statements: procedural and object approaches, DDD, use case, user story and others.