When you are on the watchface, a widget can be seen when you use the up/down buttons. They are meant for quick views of things. A device-app, with show up with activities like "run", etc, when you press start from the watchface.
To further on Jim's explanation, apps basically take over the entire user interface of the device, keep running until you exit them, and have many more capabilities than widgets. A widget would be used for something like quickly checking the weather where as an app would be for something like tracking a run or a full round of golf.
