Solid explanation of the distinction between these three sub domains is explained in an article by NVIDIA.
“Artificial intelligence is the future. Artificial intelligence is science fiction. Artificial intelligence is already part of our everyday lives. All those statements are true, it just depends on what flavor of AI you are referring to. For example, when Google DeepMind’s AlphaGo program defeated South Korean Master Lee Se-dol in the board game Go earlier this year, the terms AI, machine learning, and deep learning were used in the media to describe how DeepMind won. And all three are part of the reason why AlphaGo trounced Lee Se-Dol. But they are not the same things.
The easiest way to think of their relationship is to visualize them as concentric circles with AI — the idea that came first — the largest, then machine learning — which blossomed later, and finally deep learning — which is driving today’s AI explosion — fitting inside both.”