JAR files allow to package multiple files in order to use it as a library, plugin, or any kind of application. On the other hand, WAR files are used only for web applications.
JAR can be created with any desired structure. In contrast, WAR has a predefined structure with WEB-INF and META-INF directories.
A JAR file allows Java Runtime Environment (JRE) to deploy an entire application including the classes and the associated resources in a single request. On the other hand, a WAR file allows testing and deploying a web application easily.