A case study is a write-up of one real project in three parts: the client's challenge, your solution and the result. Companies publish them on their sites, put them into proposals and decks, and send them in emails. A case study answers the question prospects rarely ask out loud: “Have you done something like this for a company like mine?”
A service page says what you can do. A case study shows that you did it, and backs the claim with specific actions and numbers. That's why it works in two directions: a hesitating buyer reads it, and search engines and AI assistants quote it when someone asks for an example in their industry.
People search for this work under different names: “case study writing,” “case study examples,” “business case study template,” “how to write a case study.” They are all entrances to the same thing: a client story on a page, with an honest result.