Can run mobile-style apps in the area known as the start screen, while running traditional software in the more familiar desktop.

The correct Yes, mobile-style apps can run in a personal computer's desktop.

That is possible by means of a desktop application called emulatator. An emulator like Bluestacks allows a personal computer to run mobile-style apps by acting as a virtual drive in the personal computer's harddisk. 

Emulation is successful if the system requirements of the mobile-application is met by the personal computer's system attributes such as Random Access Memory abundance, Random Access Memory speed, Processing speed (in some cases core abundance e.g. core 2) etc. 

Some mobile-applications do not work in the personal computer's desktop, however, if this application requires platform specific functions such as mobile device's network provider etc.

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Database uses the approach of programming while both the data and the processing instructions are stored in the database.