It could be explain in very difficult, so waste your timefor reading. However, Jerry Blogger is a straight forword person and want to save your time.
Gadget=Widget, but Widget=/=Gadget
Widget in Computer Programming is a reusable element of a graphical user interface that displays an information arrangement and provides standardized data manipulation.
Gadget is a mini-applications for specific web-site or platform. For example, iGoogle.