Big Data 
Big data is data sets that are so voluminous and complex that traditional data-processing application software are inadequate to deal with them. Big data challenges include capturing data, data storage, data analysis, search, sharing, transfer, visualization, querying, updating, information privacy and data source. There are a number of concepts associated with big data: originally there were 3 concepts volume, variety, velocity. Other concepts later attributed with big data are veracity (i.e., how much noise is in the data)  and value.
Data Science 
Data science is an interdisciplinary field of scientific methods, processes, algorithms and systems to extract knowledge or insights from data in various forms, either structured or unstructured, similar to data mining.