Data Analytics: It is the application of a mechanical or algorithmic process in order to derive insights. In other words, it performs runs through various data set to find meaningful correlations.
Data Analysis: It is a heuristic activity where the analyst scans through all data to gain some insights.
Data Mining: It involves bringing all the data together to discover unknown trends and correlations.
Data Science: It is a multi-disciplinary field which uses scientific process and algorithms to extract useful knowledge and insights from both structured and unstructured data.
Machine learning: It is the ability of a system to automatically learn and improve or modify based on past experiences without being explicitly programmed.
Big Data: They are large data sets which are analyzed to reveal patterns, trends, and associations which are specially related to human behavior an interactions.
Hope this helps!