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In a way, yes. Java applets are just a special case of Java classes, specifically they are subclasses of the Applet class. JSP is a combination of XML tags and Java code that is dynamically compiled into Java classes by the server.
Yes, Java is a language, but the name also refers to the entire Java platform including the class library and virtual machine.
Java wasn't designed with any specific purpose in mind, and indeed you will find all kinds of programs written in Java. Of course, it does enjoy a good share of the web application market and probably more than any other general-purpose language.
Simply Java is a Programming language and JSP is a scripting language (server side)
Java can be used in web sites as Applets JSP is designed to web applications
Java is inherited from C programming language so it has the same syntaxes and concepts like it
Java is most similar to C#, they're both syntactically similar and get compiled to an intermediate language rather than native code (for Java, it runs on the Java Virtual Machine, for C# it's the Common Language Runtime). JSP is most similar to ASP.
Java's another programming language, it's also the world's most popular language. Try the wikipedia page for it
Java applets are written using the Java programming language. JavaServer Pages (JSP) are programmed using a mixture of "scriptlet elements" (Java code) and "markup" (usually HTML or XML) to serve data-driven ("dynamic") web pages.
Java is a high-level programming language.
Java is used to write applications for a variety of systems, including NASA vehicles for the exploration of Mars, business-oriented applications and data-driven web pages.
Java can be compared to programming languages such as Microsoft's C# (modeled after Java) or Objective-C (an object-oriented extension to C) due to the fact that programs written in Java, C# and Objective-C generally depend on a Virtual Machine installed on top of the operating system to execute.
JavaServer Pages are the Java community's answer to PHP and Microsoft's ASP.