There are no "two versions of Android". That's an unnecessary confusion of the situation.
There is Android, which is a complete open source operating system tailored for touchscreen devices. It is completely open source and in principle has no dependencies on any piece of propietary software to function. Android is not usually distributed with just its open source components, however.
There is Google Play Services. This a propietary set of applications and system services that interact with Google's cloud services. Since Google's cloud services are popular - most significantly the Google Play Store for Android apps - these services almost always come bundled with devices on the market. Android and Google Play Services together are also often called "Android" (even by Google itself) which is the cause of the confusion. There is a clear difference between the two, however.
Then there are further customizations in themeing, user interface components and applications made by vendors and carriers.
The problem of bloatware is that Google has only felt responsibility for Google Play Services; the other software on the system, including Android, was the responsibility of the carriers and the vendors. Android is developed by Google as an open source and popular foundation from which to provide its services - either from Android's web capabilities or from its bundled applications.