Last month, Amazon (NASDAQ:AMZN) announced several new models of its Kindle Fire tablet, including the $99, 6-inch Kindle Fire HD and an updated version of its full-size, Kindle Fire HDX. Both tablets ship with the latest version of Amazon's operating system: Fire OS 4, "Sangria."

Sangria adds several new features to Amazon's tablets, including, most notably, "Family Library" -- families with multiple Kindle devices will be able share some of their digital purchases among themselves. Though it may seem like a small change, it was a necessary one -- the latest version of Apple's (NASDAQ:AAPL) mobile operating system, iOS 8, offers similar functionality.

Apple challenges Amazon
Back in June, at its Worldwide Developers Conference, Apple introduced Family Sharing -- a new feature included in iOS 8. At the time, I noted that Family Sharing appeared to be a direct challenge to Amazon's digital goods business, particularly its digital books business -- the ability to share digital purchases with family members stood out as a key advantage: Buyers -- who may have otherwise chosen a digital Kindle book from Amazon -- could be enticed to purchase an iBook from Apple instead.

But Amazon has quickly fired back, neutralizing whatever advantage Apple may have had. With Family Library, Amazon customers will be able to share their digital purchases across as many as six linked accounts.

Family Library should help Amazon maintain its dominant market position in digital books. Apple has emerged as a competent rival, but Amazon still leads, with an estimated market share of around 60%.

Family Library vs Family Sharing
Nevertheless, Amazon's Family Library isn't perfect, and Apple's Family Sharing has a few advantages over Amazon's alternative when it comes to other forms of media. Amazon's Family Library works with digital books, audio books, apps, and Prime Instant Video, but it won't work for purchased movies, TV shows, or songs. Apple's Family Sharing, in contrast, offers all these things and more, including the ability to see family members' current geographic locations.

That said, Apple's Family Sharing requires all members of a given family to use Apple-made products, a relatively high barrier to entry. Amazon's Family Library, in contrast, is far more flexible: Amazon would probably prefer its customers own its Kindle Fires, but if they don't, it's not an issue, as Amazon's Family Sharing feature is slated to arrive on Amazon's mobile apps, including its Kindle app for Apple's iOS, later this month.

Two different goals
In an interview with Charlie Rose last month, Apple's CEO Tim Cook downplayed his company's rivalry with Amazon, instead citing Google as Apple's chief competition. Amazon may not be Apple's primary competitor, but when it comes to digital goods, they certainly compete for sales -- Family Sharing and Family Library serving as the latest example.

At the same time, the two systems highlight the relative differences between the firms: Whereas Apple is trying to entice customers to purchase its gadgets, Amazon is looking to cultivate additional sales of its digital goods.

The prospect of shared iTunes, app and media purchases, as well as geographic location and parental controls, could keep entire families loyal to Apple's product line, choosing Apple-made mobile devices over alternatives. Amazon may have been caught in the crossfire, losing digital book sales to Apple in the event that families looked to take advantage of this new feature, but Family Library could ensure that doesn't happen.

Family Library isn't a perfect retort -- the lack of music sharing won't help Amazon capture any loyal iTunes customers -- but seems more than good enough to keep Amazon's existing Kindle customers loyal.

Sam Mattera has no position in any stocks mentioned. The Motley Fool recommends Amazon.com, Apple, Google (A shares), and Google (C shares). The Motley Fool owns shares of Amazon.com, Apple, Google (A shares), and Google (C shares). Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.