However, Apple applied to register "App Store" as a trademark in the U.S., and the U.S. Patent and Trademark Office approved the application. That said, Microsoft has appealed to the USPTO Trademark Trial and Appeal Board, in an attempt to have Apple's trademark application dismissed, basing its argument on the genericness of "App Store."
In its lawsuit against Amazon.com, Apple said that it contacted Amazon three times and demanded that the online retailer cease using the name and that Amazon had not “provided a substantive response.”
The fact that the Amazon AppStore is reported to use the term without a space between the two words App and Store is apparently not enough differentiation. Kristin Huguet, a spokeswoman for Apple said that “We’ve asked Amazon not to copy the App Store name because it will confuse and mislead customers.”
The Amazon AppStore is Android-only, and can exist because Google allows applications to be installed on Android devices as long as a certain setting in the OS is enabled. AT&T, however, removes that setting completely from the OS, so unless Amazon.com makes certain allowances (allowing the app's APK file to be downloaded to a computer), there won't be any workaround for AT&T users.