Exiting an app using the "back" button (arrow button) will cause the app to do what it does when it closes.
Normally this is a "save your data", maybe it prompts you, maybe it does it automatically.
When you restart the app, your data may be loaded automatically or maybe you need to select a menu item to reload the data.
It all depends on the app.
If you switch to app_B when app_A is still running, using the square-key or otherwise, the app that was running (app_A) is supposed to remember its state and pick up from where you left off when you switch back to it since it was not closed but "paused". How well the app does that is up to the individual app.