Windows Phone Silverlight 8.1 is a 'continuation' of Windows Phone 8 Apps (apart from native apps and some exceptions, most of WP8.0 apps were Silverlight 8.0). It gives more possibilites with little change to your code, you can read more here at MSDN:
The Windows Phone Silverlight 8.1 app model gives Windows Phone 8 developers access to some of the newest features available in Windows Phone Store apps without significantly modifying existing Windows Phone 8 code.
When developing Windows Store apps under 8.1 there are two main paths: Windwos RunTime Apps and mentioned Windows Phone Silverlight 8.1 -> MSDN. Both have advantages and disadvantages. Windows Runtime Apps can be far more easily ported to other devices, you will also find some API's available only for runtime apps and some other Controls under WinRT. You may also want to read about Universal Apps.
As for Silverligt you may also look at this video.
More about programming concepts you will find here at MSDN.
So when you find such a sentence:
Applies to: Windows Phone 8 and Windows Phone Silverlight 8.1 | Windows Phone OS 7.1
it means that it can't be used with WP8.1 RunTime Apps. And vice-versa:
Minimum supported phone Windows Phone 8.1 [Windows Runtime apps only]
only for RunTime apps. Good example here is different navigation in those two models.
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