SDK - software development kit
ADT - Android development tool
SDK includes sample code, libraries, system images, platforms and so forth. You can download and install the Android SDK for details.
ADT is a plugin for Eclipse. If you download an Eclipse from Eclipse official website, you cannot develop Android app until you install the ADT plugin. It includes DDMS, logcat, and so forth. Using ADT, you can create and build an Android app quickly.
As a matter of fact, you don't need to download them separately. Google provides the
ADT bundle[
^], which has already contained everything you need for development. You can also download the
Android Studio[
^] for app development.