There are several apps for the Windows phone that aren't available at the Windows store for PCs, including certain games.
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The Windows feature that allows you to quickly display two apps side-by-side is called "Snap Assist." You can activate it by dragging a window to either side of the screen or by using the keyboard shortcut Windows key + Left or Right arrow. Once one app is snapped, Snap Assist will show you the other open windows, allowing you to choose which one to fill the remaining space. This feature enhances multitasking by enabling easier comparison and interaction between applications.
Apps is short for Applications, the equivalent to Programs in Windows.
As of 2013 the catalog of Windows 8 phone apps has not been made available on the Windows 8 OS.
Games
You can find a complete list of all apps that are allowed on your PC with Windows 8.1 on the Windows (dot) Microsoft website.
The reason why Windows 8 apps may stop working is that they have not been updated. You may be forced to reinstall the apps in order to get them working again.
You can find tips on Troubleshoot Windows Store apps on Surface by visiting microsoft.com/surface/en-gb/support/apps-and-windows-store/cant-find-or-install-windows-store-apps
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If you have iTunes for Windows and have iOS apps saved on your Windows computer, you cannot actually use the apps in any way on the computer. The one exception would be if you jailbreak, you can be able to use anything on your iPhone's display on your computer. I am not sure how that works, but I know it is possible.
Windows 1.0 to Windows 3.0 could only run 16-bit apps. Windows 3.1 could run certain 32-bit apps through call thunking.