You are right that most people think of white box (structural) testing only with respect to code. While tests indeed should address what the system should do, that is the focus of black box (functional) testing. White box testing instead is mainly a method to more systematically confirm that what has been written has been exercised.

Because white box testing of code requires knowledge of the code, it generally is considered to be outside the realm of independent testers and thus the sole province of developers. However, although most developers’ testing is based on exercising the code they have written, few developers know of white box testing’s methods for systematically exercising the code, let alone how to do it.

Unfortunately, few testers and analysts recognize that they also can use white box testing techniques, which are especially useful for testing use cases, menu structures, workflows, and business logic.