Safari for macOS lets you view the kind of data cached locally by websites in your browser. Select Safari > Preferences > Privacy, and then click Manage Website Data, and you can see the kind of data stored by every site. It can include Cache, Local Storage, Databases, Cookies, and much more. You can select items to remove them, or even go nuclear and click Remove All.
Those are different categories of local storage, but they’re all managed by the Web site with the permission and mediation of the browser. Cookies is the most likely one to see, as cookies typically contain a login token used to keep a session going as you navigate among pages, or tracking data used by advertisers.
