"Amazon has begun improperly using Apple's App Store mark in connection with Amazon's mobile software developer program," Apple said in the complaint cited by Bloomberg. "Amazon also plans to use the name with a mobile software download service, the complaint states," according to Bloomberg. Apple's App Store offers downloads of software programs from the company and third-party developers, for users of its iPhones, iPods and iPads. There have been more than 10 billion downloads through the service since it was started in 2008, Apple claims in its suit.