Weather and stocks are cool, but just imagine having the option to have a widget that allowed you flick through your most recent tweets or facebook updates. I think this is the next step
I wouldn't say so, Notifications are a single piece of uninteractive information from an app, once its been delivered, that is the notification. Widgets are dynamic and can change on the fly, like weather or stocks, and the use can have small scale interactions with them to access specific information.