Amazon launched their Appstore back in March of 2011 and shortly after, Apple came forward with claims of false advertising. According to Apple, people could end up being confused between the Amazon Appstore and their App Store. And well, previous history aside, it looks like Amazon has taken a small victory in this case.
According to a recent Bloomberg report, Amazon has won dismissal of Apple's false advertising claim. The ruling comes from U.S. District Judge Phyllis Hamilton in Oakland, California, who said that she found; “no support for the proposition that Amazon has expressly or impliedly communicated that its Appstore for Android possesses the characteristics and qualities that the public has come to expect from the Apple APP Store and/or Apple products.”
Part of this decision is likely a result of comments made by both Steve Jobs and Tim Cook. Amazon argued that both used the term "app store" to discuss the competition. According to a Reuters report, Steve Jobs once referred to the "four app stores on Android" and Tim Cook mentioned "the number of app stores out there."
Basically, it seems like there was little reason to believe that anyone would confuse the two app stores. Keep in mind, that is not the complete case though and this ruling deals only with the false advertising claim. The other side stems from a November 2011 trademark claim. On this front, Apple is seeking trademark on the 'app store' name.