API --- Application Programming Interfaces (000's of lines of codes which help you to make your own programmes) APPLET --- A small downloadable program which performs some task at the client end like calculation, sorting, etc etc. APPLICATION --- Just any other software application
Applets run in a browser. They do not have to be installed. They have their own "format" as well. Instead of a method main() they use methods init(), start(), stop() and destroy(). Applets are much more limited in what they can do. in particular they cannot read or write files on the client system, cannot write on the server system and can only connect directly with the server they are loaded from. you can however use signed applets(which allow more) if the client accepts.