That depends what you mean by "Windows 8 apps". Desktop applications, such as Photoshop, iTunes, Dreamweaver etc will not run on RT but apps from the Windows Store (such as Xbox Music, Netflix, Twitter, SkyDrive etc) will work.
Windows RT: It's a lot like Android and iOS. It can run touch screen apps and games downloaded from the app store. Examples of apps are Temple Run, Evernote, and Angry Birds. However, it cannot run desktop apps and games, which are apps you can install in Windows 98, XP, and 7, like Counter Strike, DOTA, and Google Chrome. This OS is designed for cheap tablets and is mostly used for playing games. It cannot run on Intel or AMD CPUs - instead, it runs on CPUs used for smartphones.
Windows 8: Basically the sequel to Windows 7. It can run desktop apps and games and apps from the app store. This OS is designed for desktops, office computers, and laptops. It runs on Intel and AMD CPUs.
I can understand your confusion because the two OS look exactly alike, yet on the inside, they are very different.