With over 500 million iTunes accounts with credit cards attached (2.5 times as much as Amazon, to realize how many they have), with iBeacon, and TouchID authentication coming to all of Apple's devices soon enough, it's only a matter of time before Apple starts letting other websites and services to integrate the iTunes payment system, so people can pay with their Apple accounts. This could make Apple absolutely huge in payments, and Google is missing out, by not being aggressive enough with their payments systems (Google Wallet being the most recent one).
Google entered online payments a long time ago when it launched Google Checkouts to compete against Paypal. Unfortunately, as soon as they realized it may be tougher to beat Paypal than they thought, they pretty much gave up on it. Checkouts was barely updated for a few years straight, and Google didn't really try to promote it anymore.
That was a huge mistake, because then they created Android and the Android Market/Play Store, but they didn't have a popular payments system of their own that people are using, so they can buy with "one click" apps from the store.
Apple on the other hand started out with a relatively huge customer base that had their credit cards tied to Apple's iTunes accounts, since the iPod days. So when Apple launched the App Store for iOS, people immediately started buying apps with 99 cents or more, just like they would buy songs for their iPods. This, in turn, led to many developers being interested in developing for iOS, knowing they can make a lot of money.
To this day, I think not having a popular payments system is what hurts the Play Store the most, and why revenue per app is significantly lower than on iOS. When people don't have their credit cards already tied to Google accounts, then it's a huge hurdle to convince them to pay that $0.99 for an app, and I imagine most people just look for the free alternatives instead of bothering with that. Not to mention that the more recently launched Google Wallet is not a very strong brand that most Android users know about, which means that even if they want to buy apps, they may be reluctant to give their credit card info to Wallet.
At least Google finally started asking Android users to sign-up for Google Wallet starting with Android 4.0, but it was still done relatively late, and they haven't done all that much promoting of Wallet to other services, so people can see Wallet all over the place. That way they can maybe buy some other product online with it, and then just simply use it to buy from Android's Play Store, too.
Google needs to find a way to make all Android users use Google Wallet, and they need to do it soon, before Apple becomes too ubiquitous in payments. This is why I believe Google is doing the right thing taking control of Android, so they can launch these sort of services to all Android users, not just to Nexus users or Motorola users. It's the only way to fix fragmentation.
When Apple launches something new everyone pretty much assumes it will become popular. Why? Because Apple has hundreds of millions of devices out there, and with just one update, they can push that feature to all of them. Google can't do that right now, and it needs to be able to do that to compete effectively.