Design Differences

So I'm building myself a little UI kit, and I have now build the alert, notice, and modal objects and they each have a specific reason for their existence.

The alert is much like the Android Snackbar it's an alert saying "this thing has happened" stays up for a period of time and allows for the user to have a simple action feedback like UNDO.

The notice on the other hand is more like Android's Toast it's a simple message display that stays up for a period of time (shorter than the alert) and has no user feedback.

The modal is just what it sounds like its a pop up window with a larger view area and stays up until the user dismisses it. It can have multiple feedback options positive, negative or neutral. The modal has a full page overlay behind it with opacity set low so its obvious its there but you can still see the content on the page. So you cannot interact with the content on the page until you've dismissed the modal in some fashion.

My question is about the other type of modal commonly called a dialog and a prime example is jQuery UI's dialog box. its like a modal but with now overlay behind it allowing to user to still manipulate content on the page behind it without dismissing the dialog. (I realize jQuery UI has an option you can pass in to the dialog to make it a modal.) but my question it when would you ever not want that to be the case? When would you want the user to mess with stuff on the page behind the dialog without dismissing the dialog?