To display artificial intelligence (AI) means that machines need to exhibit intelligence the way human being do; that is, being able to learn, understand and use the knowledge learned to carry out one specific functions. This could be something like a prediction or recommendation based on what it learned. When people talk about artificial intelligence vs machine learning, they should really consider the machine learning part as a subset of AI as a whole.
Machine learning means that the machine has the ability to automatically learn from data without needing any explicit programming or subject matter expertise.
The learning part is performed by algorithms that implement mimic aspects of learning. These algorithms use decision trees, neural networks or regression analysis for this purpose. The results are all the relationships, correlations, patterns and other salient information from a given set of data.