Structure widget is displayed in a separate tab on a Project page if the project is enabled for Structure.
The widget on the project page is the standard fully functional structure widget and has the same set of functions you can find on the Structure Board (except for Perspectives).
By default, structure tab displays the current structure (structure that was opened last). You can quickly switch to another structure by clicking the structure name and selecting the desired structure.
Project Page Options
If you wish, you can make the widget open with the structure that is defined as a default structure for this specific project.
To do that, click the options gear button in the top right corner and select the Auto-switch option. The changes are saved to the server and applied immediately.
If you are the Project Administrator, the options dialog will also show the link to a page where you can change the default structure for your project.
The default value for this option can be configured by JIRA Administrator on the Structure Defaults page.