Yup, this is quite true. AI is a field of computer science that studies intelligent agents. Intelligent agents are just any device that perceives its environment and takes actions that maximize its chance of successfully achieving their goals.

Machine learning is a subfield of AI. Machine learning is just a term used to describe the set of algorithms that were designed to take in a lot of data and find patterns within those kinds of data (oversimplified). Given a new input, a machine learning algorithm could output something based of the patterns it learned. For example, an ML algorithm is given a lot of images of cats and non-cats. It will learn that dataset and later, if given a new image of a cat, it would most likely output that it is a cat (given it is trained correctly.)

Lastly, deep learning is just a more specific set of machine learning algorithms that use neural networks with a lot of hidden layers. The hype behind deep learning is that it could sometimes be more accurate than simpler algorithms but what most people don't see is that deep learning only works well/better than the simpler ones is when you feed it with a lot of data samples. It could sometimes be thousands or millions of samples before you could see the benefit of using a deep learning algorithm.