As per the subject, there is a type discrepancy in the API.
Now, Application.PersistableType is actually defined to be the same as Application.PropertyValueType, which is fine, but Background.getBackgroundData and Background.exit should still be listed as using Application.PersistableType for consistency.
In addition, it would be REALLY good if Application.PersistableType (and/or Application.PropertyValueType) could be extended to include Graphics.BitmapReference and Graphics.FontReference so that these objects can be passed to the foreground through Background.exit. I can't see any reason why this shouldn't be done. It otherwise requires using Storage.set/getValue, which is a heavy-handed approach for sending a tiny object.