Typically, the term Data Mining refers to the analysis of data from different perspectives and transforming that data into useful information, establishing relationships between data or identifying patterns. This information can then be used by companies to increase revenue or reduce costs. They can also be used to better understand a customer base in order to establish better marketing strategies.
Machine learning (ML) is a category of algorithm that allows software applications to become more accurate in predicting outcomes without being explicitly programmed. The basic premise of machine learning is to build algorithms that can receive input data and use statistical analysis to predict an output while updating outputs as new data becomes available.
In practical terms, deep learning is just a subset of machine learning. It technically is machine learning and functions in a similar way (hence why the terms are sometimes loosely interchanged), but its capabilities are different.
Basic machine learning models do become progressively better at whatever their function is, but they still some guidance. If an ML algorithm returns an inaccurate prediction, then an engineer needs to step in and make adjustments. But with a deep learning model, the algorithms are capable of determining on their own if the prediction are accurate or not.