Apple has sued Amazon.com because of the name "App Store." Amazon.com has recently launched a new Android Marketplace called the Amazon AppStore.
Now here is the problem, Apple had registered "App Store" as a trademark in the U.S. which the U.S. Patent and Trademark Office approved the application. Microsoft has been trying to appeal to the USPTO Trademark Trial and Appeal Board, in hopes to dismiss Apple's trademark.
In Apple's lawsuit against Amazon.com, Apple said they contacted Amazon several times and demanded that they cease using the " App Store" name however Amazon has not provided a substantive response. In Amazon's defense, they claim that they use the term without the space (AppStore).