Somehow Google managed to bring shared accounts to iOS, although it's not exactly clear how. The latest version of the YouTube app and the new AdSense app bring the following features:
- support for multiple Google accounts
- quickly switching between accounts without entering your password
- the accounts are shared between Google apps.
If you enter the credentials of a Google account in the YouTube app and then open the AdSense app, you'll find the new account and you can sign in without entering the password. If you remove an account, it will be removed from the other Google apps that support this feature. I assume that most Google apps for iOS will be updated to use this brilliant feature.
YouTube's help center informs that "if you've signed in with another Google app on your iOS device, you may see this account listed." This means that the accounts are associated with your device, so maybe Google uses an unique ID for each device. iOS devices have unique IDs called UDIDs, but they can no longer be used in iOS 7. App developers can use vendor IDs, which are identical for the apps from the same developer and they "uniquely identify a device to the app's vendor". It's interesting to see that "the value changes when the user deletes all of that vendor's apps from the device and subsequently reinstalls one or more of them."