Computer Science and Data Science, though being interdisciplinary fields of science, are two completely disparate concepts. Computer Science is the broad study of all computational systems which includes both hardware and software. Therefore, implementation of computational algorithms and processes in any domain (be it microprocessor chips, artificial intelligence, compiler designs etc.) come under the purview of computer science.
Data science is a small subset of computer science which deals in the application of computational algorithms and machine learning to data to derive insightful trends & patterns in data which can be used to predict the future & shape business decisions accordingly.