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While the term applet is sometimes used to describe small programs included with a computer's operating system, it usually refers to Java applets, or small applications written in the Java programming language. Unlike ordinary applications, Java applets cannot be run directly by the operating system.
Applet is a part of Core JAVA and Servlet of Advance Java. Applet is client side program and Servlet is Server side. When Applet runs it take the resources of client whereas Servlet is processed at server. An Applet's class, jar files can be accessed and downloadable by client but not so in case of servlet.