Difference between iTunes Store and Apple TV app

I was planning on buying the digital version of the extended edition of the LOTR trilogy. At first I looked at the TV app, as I thought all video content would be on there. However I only found the normal edition of the movies there. At the iTunes Store I could find the extended edition and it even was cheaper than on the TV app. So I don’t quite know anymore what the difference is and where would be best to buy it. Can anyone clarify?