You can use any fermentable to carb with. Corn Sugar is what most kits and many homebrewers use, but table sugar, malt extract, anything can be used. You just have to figure out the right ratio for whatever you're using.
I use different things depending on the beers. For example I prefer to use table sugar over corn sugar or anything else, for Belgian Beers and Certain Historical styles. I think it give a rockier head with tighter white bubbles.
You can use any fermentable for priming. I give detailed info on priming with alternative primers including fruit juice (including the link to the podcast,) and other sugars in my bottling stickey- Scroll to the lower half of this post.
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