IDE

An IDE or Integrated Development Environment is a software to run and execute your code. It has a lot of features which make development faster like code completion, organizing your project, searching for resources in your project, debugging your code etc. It can also be extended by installing plugins. For example, there is a plugin called key promoter which helps you learn keyboard shortcuts for the IDE by showing a modal window with the shortcut when you do an action/sequence of actions 3 times via mouse. For Android development the de facto IDE is Android Studio. It used to be eclipse previously but Google is not supporting it anymore. Android studio is a customized version of Intellij Idea by Jetbrains . Below is a photo of the Android Studio interface.

Android SDK

Android SDK (software development kit) is the set of libraries and resources (documentation, images, emulator etc ) that are required for development of application. A library is a collection of useful code which can be shared across easily. Imagine someone has written some code to perform some mathematical calculation. If they want to share their code to others, the easiest way would be to bundle it as a library and share.Android SDK comes bundled with android studio but can be downloaded separately and configured along.