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In a sense, PhoneGap apps are actually NOT Web apps, they are native apps built using Web technologies.

No; they're webapps embedded in web browser aka WebView. Refer http://phonegap.com/2012/05/02/phonegap-explained-visually/

No they aren't, they use hooks to native phone functions. You can't write once, run everywhere.

They're native apps written in HTML, CSS, and Javascript. That doesn't mean they're web apps.