Difference between Apple Store and iTune store

iTunes is the online market place where you can buy music, movies and other apps and software for your iDevices

The corresponding thing on the Mac is the Mac App Store

Apple stores are usually referred to the physical locations of stores (usually in malls or large shopping areas) that mainly sell hardware - computers, screens, accessories, iPhones etc - the stores do offer a trouble shooting area called Genius Bar staffed by Apple employees with limited repair options (eg battery and screen replacement for iDevices)

iTunes store sells/rents digital media. App store sells applications software.

Apple Store can also refer to the App that lets you buy devices, computers,, accessories and other hardware from Apple as if you were in a physical store directly from your iPad, iPhone or iPod Touch.

Apple Store (Devices, Hardware):

iTunes Store (For Media: Movies, Tv Shows, Music, Podcasts etc..)

App Store (For Apps, software)