In design mode, you design your app and you can work with widgets by adding/editing and moving them. This means you can work with all available options and widgets and do any changes while in design mode.
In App mode, you cannot work with widgets. In app mode, we can’t drag and drop the widget to the mobile editor we use the sections instead. You can see how your design looks like as in real device and you can edit and change options for a selected widget as shown in below screenshot: