React is a JavaScript library, supporting both front-end web and being run on a server, for building user interfaces and web applications.
It follows the concept of reusable components.
React Native is a mobile framework that makes use of the JavaScript engine available on the host, allowing you to build mobile applications for different platforms (iOS, Android, and Windows Mobile) in JavaScript that allows you to use ReactJS to build reusable components and communicate with native components further explanation
Both follow the JSX syntax extension of JavaScript. Which compiles to React.createElement calls under the hood. JSX in-depth
Both are open-sourced by Facebook.