Machine learning is a field of computer science that uses statistical methods like logistic regression, linear regression, clustering etc to create programs that improves itself over time. That is the program that learns itself over time, which is a part of Artificial Intelligence.
Nowadays Machine Learning is now replacing the explicit programming which is Inflexible, Costly and Can’t Adopt to the change in need for the environment.
Data Science — it might not have nothing to do with learning as machine learning because it is a data driven science and requires mathematical as well as statistical algorithms to derive the required solution and 90% of the programmers don’t have, as they come from computer science background not from Mathematics Background. Therefore in Machine learning it concentrates more on programming then understanding the complex mathematical and statistical concepts of Data Science.
I believe you have heard the world Data Scientist quit often in the field of Data Driven Jobs. Data Scientist is the person who actually uses various way by meaning of tools and complex algorithms to find the remedy of the cause. He encompasses with various skills from technical programming, to implementing complex algorithms to answer the complex situations.