The focus shifted from WebApps to Native when the App Store was unveiled with the release of the iPhone 3G with iOS 2.0.1, which was introduced on June 9, 2008 at the WWDC.
Initially Web Apps were intended to be used with the first iphone, but the major shift took place with the release of the dedicated iOS (or iPhone OS as it was called then) Software Development Kit announced at the iPhone Software Roadmap event on March 6, 2008. The SDK allows developers to create applications using Xcode that will natively run on the iPhone, iPod Touch and iPad. Even prior to that, the included applications were written natively despite the fact that Steve Jobs once remarked:
The full Safari engine is inside of iPhone. And so, you can write amazing Web
2.0 and Ajax apps that look exactly and behave exactly
like apps on the iPhone. And these apps can integrate perfectly with
iPhone services. They can make a call, they can send an email, they
can look up a location on Google Maps.
And guess what? There’s no SDK that you need! You’ve got everything you need
if you know how to write apps using the most
modern web standards to write amazing apps for the iPhone today. So
developers, we think we’ve got a very sweet story for you. You can
begin building your iPhone apps today.
The difference is as simple as that age old difference between "interpreted" and "compiled" applications.
Native apps are written using lower level languages (Objective C, C, C++ using Xcode development environment) and are compiled against APIs that are designed to extract maximum speed and efficiency using algorithms and functions that are written specifically against the hardware they are intended to be run on. Compiling code into directly executable machine code almost always the fastest method of execution for a given software task.
In the specific case of Twitter, the twitter app is simply not using webkit, it's using other routines written in objective C which are again (the key word I suppose) optimised for the best results in a way nothing in a browser can achieve. Oddly, I think the Facebook native app is actually a thinly veiled wrapper around a webkit UI.