"A widget is a piece of reusable code that you can plug into virtually any website."
You can use it in any blog using html's , copying the html code and pasting it some where is belongs to widgets.
"A Gadget is a tool that can only be use as a tool"
Using gadget we cant use html codes, we cant copy it to other places.
I hope my short article about Widgets and Gadgets, helps you to find the different between them.