Android Enterprise is Google's official framework for managing Android devices and apps in the workplace. It was introduced in Android 5.0 (originally branded "Android for Work" and is built into all GMS-certified Android devices running 5.0 or higher. Compared to the older Device Administrator model, it provides a more secure and flexible approach to device management.
MDM (Mobile Device Management) is the broader category — the practice and tooling for centrally enrolling, configuring, securing, and monitoring mobile devices. Android Enterprise is the set of APIs and management modes that an MDM/EMM platform plugs into on the Android side. In other words, your MDM is the console and policy engine; Android Enterprise is the native OS framework it uses to actually enforce those policies on Android devices. An Android Enterprise solution integrates an EMM console, Android Device Policy for applying policies, and Managed Google Play for app management.