This is mostly a question of terminology. The previous answer explains that linguistic testing is about controlling the language localization of a product in context, meaning texts within the UI (app screens, messages, and notifications).
In some companies, localization testing is the same as linguistic testing, whereas others prefer to include into localization testing the functionality testing of the product. In this case, localization testers are required to report not only linguistic errors and inconsistencies but also functionality bugs.
While testing is typically linear for websites, functionality testing for software and apps usually covers a brunchy decision tree and requires test scenarios and cases.
We usually discuss the scope of the required testing activities with the client. The client provides our specialists with context (localized screenshots, Figma screens, or other dedicated professional testing apps). If the client prefers that our specialists also perform functionality tests, we will discuss the test case.
In either case, our localization testers report any bugs that are revealed in addition to linguistic errors.