Although these terms are used interchangeably, they are not the same. Essentially Deep Learning is a type of Machine Learning, and Machine Learning is a type of Artificial intelligence.
Artificial intelligence is all about making computer programs mimicking human intelligence for some specific tasks.
Machine Learning is a part of Artificial Intelligence, and represents computer algorithm which performs automatic configuration of its internal parameters based on example data in order to perform some task.
Deep Learning is a type of Machine Learning which is based on using artificial neural networks which are inspired by the simplified computational models of brain. At the moment it is the most popular AI technique, thanks to successful applications in computer vision, language processing, and many breakthroughs in accuracy.
It can also be said that Machine Learning is a subset of Artificial Inteligence, and Deep Learning is a subset of Machine Learning, since Artificial Intelligence includes many techniques other than Machine Learning, and Machine Learning includes many techniques other than Deep Learning.