Java Applets vs Stand-Alone Applications
Applets:
These are Java applications that download from a web site and run inside a web browser (assuming it's Java enabled). The advantage here is that you're always getting the latest version (since it's downloaded from the source every time), and you can use any computer (e.g., cyber cafe in a foreign country) to access the application. The disadvantage is that the download can be time consuming if the application is large, and the performance of applets is generally poorer (sometimes much more so). You also need to connect to the internet each time you run the applet (although it will remain usable, even if you disconnect, until you quit your web browser).
The following link will tell you whether you can run Java applets in your browser:
http://www.javatester.org/enabled.html
These are executable Java files (*.jar format) that are downloaded to your computer and can be used at anytime without needing an internet connection (assuming the application doesn't need to access any web-distributed resources). The only disadvantage here is that you might be using an out-of-date version, and you won't be able to access the application from someone else's computer (unless they've downloaded it too).