Data science and Big Data can overlap substantially, but understanding what distinguishes one from the other is important. The general term Big Data refers to the current explosion of data we are experiencing in the digital age, including the gathering and exploitation of large data sets and the ways that data is recorded and stored.
Data science is a more specific, academic term that refers to the various techniques used to examine and analyze massive data sets. Data science encompasses issues of statistics and statistical modeling and the way data is organized and categorized. It often focuses on finding patterns, values, and insights in massive data sets.
To simplify, data science concerns the science of information, whereas Big Data is about the application of data science to information in the real world.