This was a confirmed bug in the Windows versions of PixInsight 1.8.5. It was completely fixed in version 1.8.6. In fact, it cannot be reproduced on any of our Windows 10 working and testing machines with 1.8.6 (the problem was reproducible with version 1.8.5 on some of our machines), and has not been reported before.
If you still see differences between File > Quit and closing the application's main window, then this is a machine-specific issue, unless we can reproduce the same behavior. Actually, there is no way this can be a problem anymore with 1.8.6, since both operations perform exactly the same sequence of operations to terminate the running application.