There are dozens of E-book readers for mobile devices. The apps which are native to Apple are iBooks and Newsstand. The content in Books is sync with ‘books’ in iTune and the content in Newsstand is stored in App store. iBooks will display PDF, books, and audiobooks, while Newsstand is mainly used for subscription-based magazine and newspaper. We can obtain the content for both apps through iTune store.
There are other 3rd party apps to obtain the content for e-books. I guess that the most well-known app is kindle. kindle is the device for e-book reader as well as the name of app you can use for the content via Amazon.
Those who have multiple Amazon accounts, there seems to be a way to migrate these accounts (although I didn’t do it. アカウント結合: http://ebook.itmedia.co.jp/ebook/articles/1211/06/news012.html). Amazon offers multiple apps for reading digital books in mobile device. The main app is ‘Amazon kindle’ which allows to store the digital materials you purchased in device. Another app is ‘Amazon cloud reader’ which allows to access the materials in cloud environment. Using these apps separately allows to display the content through multiple Amazon accounts more or less.
As for E-book reader apps specific for Japanese, the apps can be downloaded for 楽天, 紀伊國屋, and many other places. some people have explored these apps such as here. The content of these apps can be synced and transferred through individual company website (they obviously require the account to do so).
As far as the amount of content available from foreign countries (Japanese in my case), most of them are more or less the same. Newsstand is definitely specialized for magazines and newspaper, as it was intended. Some companies allow the credit card from US to purchase the materials. Others do not.