Simply put, AI refers to the ability of computers to perform complex tasks and exhibit human-like intelligence. This can mean pretty much anything - from playing games to estimating the probability of defects on a production line. The concept of AI by itself does not specify which exact technology is used, but rather refers to the complexity of the intellectual task that is now performed automatically. At the same time, it is machine learning that mostly powers AI capabilities today, and thus the two terms are often used interchangeably.
Machine learning is a set of technologies that allow computers to learn from examples. Fed with available data, machine can identify underlying patterns and teach itself to perform the given task automatically. Instead of trying to explain a computer how a dog - or a surface defect in steel - looks like, one can show enough visual examples to let it figure out for itself. Same goes for being able to predict the production output learning from past process history, and so on.
The mathematics behind this approach has long been known, but its practical use only became possible with the availability of large datasets and computing power, leading to the widespread adoption in the recent years.>
This is an umbrella term that refers to the application of statistical methods for data analytics. The job of data scientist includes using advanced techniques such as machine learning, but does not limit to them exclusively. More traditional methods are also applied, and tasks may vary from building deep learning models to descriptive analysis and data visualization. This term is well-suited to define the job of an expert, but it makes sense to specify the scope and technologies when talking about specific "data science" use cases.