What is a store app?

As of December 2014, Microsoft terms are as follows:
※ In Windows 10, Xbox is also said to be covered by the Universal Windows app, which may change the term.
※ Edit December 30, 2014: Between December 19th and today, the Japanese version of MSDN page was changed to match the English version.To match this, modify the Store App to Windows Runtime App.

Japanese version of MSDN: Store appWhat is the Windows runtime app
MSDN in English: What's a Windows Runtime app?

• Store AppWindows Runtime App (Sun)/Windows Runtime App (US)
  Non-desktop apps running on Windows devices and Windows Phones
  and using Windows runtime

• Windows Store Apps/Windows Store apps
  Store appWindows Runtime app/Windows Runtime app that runs on Windows devices (PCs, tablets, laptops, etc.) and can be sold in Windows stores

• Windows Phone Store Apps/Windows Phone Store apps
  Store appWindows Runtime app/Windows Runtime app that runs on Windows Phones and can be sold in Windows Phone stores

• Universal Windows App/Universal Windows app
  Store appApplications available in both Windows and Phone stores that are Windows Runtime app/Windows Runtime app
  ※ It's not a universal Windows app, it's a universal Windows app. Perhaps to emphasize that, the first "u" may be written in lowercase letters in English.

Store appWindows Runtime app (Sun)/Windows Runtime app (US)
Non-desktop apps running on Windows devices and Windows Phones
and using Windows runtime

Windows Store Apps/Windows Store apps
Store appWindows Runtime app/Windows Runtime app that runs on Windows devices (PCs, tablets, laptops, etc.) and can be sold in Windows stores

Windows Phone Store Apps/Windows Phone Store apps
Store appWindows Runtime app/Windows Runtime app that runs on Windows Phones and can be sold in Windows Phone stores

Universal Windows App/universal Windows app
Store appApplications available in both Windows and Phone stores that are Windows Runtime app/Windows Runtime app
※ It's not a universal Windows app, it's a universal Windows app, and the first "u" may be in lowercase in English to emphasize that.

2014Added December 30, 2014
With the term change to Store App → Windows Runtime App, the following types of apps are no longer included:By following this definition, if the Windows Phone Silverlight X app and the Windows Store app are universalized (it is possible.I've done it myself, and it's in the MS apps) and I won't be able to call them universal Windows apps anymore.

• "Windows Phone Silverlight App" (for Windows Phone 7.x) · "Windows Phone Silverlight 8 App" · "Windows Phone Silverlight 8.1 App"
  Application that runs on Windows Phone and can be sold in Windows Phone Store, but not Windows Runtime App

If you write roughly, it will look like this

• Store Apps…Terms that combine the Windows Phone and Windows Store apps

• Windows Phone Store Application...Apps that run only on Windows Phone 7/8.1 (with strong smartphone elements)

• Windows Store app…Apps running only on Windows 8/8.1/ (with strong tablet elements)

• Universal app…Apps that can be downloaded and launched on both Windows Phone and Windows 8/8.1 (Of course you can develop both.)

Store apps…Terms that combine Windows Phone store apps and Windows Store apps

Windows Phone Store App...Apps that run only on Windows Phone 7/8.1 (with strong smartphone elements)

Windows Store apps…Apps running only on Windows 8/8.1/ (with strong tablet elements)

Universal apps…apps that can be downloaded and launched on both Windows Phone and Windows 8/8.1 (Of course, it can be developed in both ways)