I asked this same question and got these answers:
"A widget is an app running on your screen... such as displaying the time and weather without having to click on anything
A shortcut is simply a link to open whatever app/contact/bookmark/etc you want a quick link to" and
"Widgets are great if you look at your phone a lot thruought the day.. but if you are out and about a lot and not able to charge so often, I would not run that many. An app like the FB widget which gets an update every 1/2 hour probably wont drain too much.. it's mostly sitting around waiting for that 1/2 hour, then gets updates. But any widget that can run continuously, or get updates every minute or so, will drain your battery faster. How much is really dependend on the app. A widget app that has lots of threads running and uses a lot of cpu might drain faster than an app that doesn't do much at all (the duh factor.

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