Data Science, Machine Learning, Data Mining and Deep Learning can often be used Interchangeably. The commonality among these disciplines is a focus on improving decision making through data analysis. However, although Data Science borrows from these other fields, it is broader in scope.
Machine learning (ML) and Deep Learning focuses on the design and evaluation of algorithms for extracting patterns from data. Data mining generally deals with the analysis of structured data and often implies an emphasis on commercial applications. Data science takes all of these considerations into account but also takes up other challenges, such as the capturing, cleaning, and transforming of unstructured social media and web data; the use of Big-Data technologies to store and process big, unstructured data sets; and questions related to data ethics and regulation.
Data analysis is a part of Data Science which is mostly depended on Statistical Analysis. Statistics is a branch of science which was used to collect data and perform statistical analysis such as summarizations and present data using various visualizations. Later after the invention of Probability Theory, Statisticians started using it as one of their analysis tools. Deep Learning is a subset of Machine Learning. Deep Learning based on Neural Networks. These Deep Learning Networks are simply Neural Networks that have multiple layers of hidden units; in other words, they are deep in terms of the number of hidden layers they have.
As a summary, Artificial Intelligence is a mixture of Data Science, Machine Learning, Deep Learning, which is shown in the above picture. Each of these are very broad and includes various other fields such as Probability, Statistics, and so on.