Pure Android is
AOSP. This was the basis for Android back in the day, and Google just added a few apps for some of their online services, like Gmail, Maps, Talk, and YouTube. Fast forward to today, and the Android on the N5 is very different. Many of the apps from open source Android have been replaced by Google's own closed source, proprietary version:
music player
calendar
keyboard
camera
browser
messaging
gallery
launcher
(there could be more)
In order to use the proprietary replacement apps and the Play Store, Search, Google Now, etc., which are big draws for the manufacturers, companies like HTC and Samsung need to license these from Google. If a company decides to just use and develop from open source Android, like Amazon and several Chinese manufacturers have, they are basically "dead" to Google. And if another Google-partner manufacturer tries to also sell devices with "non-Google" Android, like Acer did, Google will threaten to cut them off, as well.
Because Android started off as open source, this is Google's way of controlling their massive stake in the OS and ensure companies continue to use "Google Android" (which they can then skin, turn into Sense or TouchWhiz, or whatever). So as we go forward, Google's Android is becoming much more different from "pure" Android.