Apple's App Store has seemingly dropped the "duplicate functionality" ban from Web browsers and has begun accepting a few third party apps, with one big caveat they are all still based on the same Webkit.
MacRumors is reporting that at least four third-party Web browsers have appeared in the Apple App Store in the past day. Edge Browser, Incognito, WebMate:Tabbed Browser and Shaking Web. However as mentioned all four of the apps Apple has approved so far are based on the WebKit frameworks provided in the iPhone SDK that is also used by Safari.
The new browsers, while being separate applications, are just different user interface designs of the built-in iPhone rendering engine - WebKit. So basically, the code in the new apps rendering the web pages is still Apple's and not really that off a "third party".
WebKit is an open source web browser engine, as well as the name of the Mac OS X system framework version of the engine that's used by Safari, Dashboard, Mail, and many other OS X applications.
Does this mean we'll see Firefox or Opera on the iPhone some time soon? Perhaps not, as Apple's SDK restrictions among other things remain in place. However as MacRumors has said,"Apple appears to be loosening some early restrictions they had applied to the App Store approval process."