(Work in Progress)
Xcode is a development environment for making apps, similar to the AI2 interface.
The iOS SDK is a software program that lets developers run iOS apps on physical phones and upload apps to the app store (for a $99 annual fee).
To start, download Xcode. One caveat of iOS development is that Xcode is only available on the Mac store. However, it is possible to download Xcode on virtual machines. Once downloaded, it is possible to start coding. However, unless the iOS SDK is downloaded, you will not be able to launch your app on a physical device or put your creation on the App Store.
Next, create an account at iTunes Connect. When prompted to enter your credit card information for purchasing the iOS SDK, make sure to use a card in your name, and not a parent or relative. If you use a parent's credit card for purchase, your info will not match the card holder's, and your purchase will be delayed for up to a few weeks. (I found this out the hard way)