JavaScripts

A scripting language developed by Netscape to enable Web authors to design interactive sites. Although it shares many of the features and structures of the full Java language, it was developed independently. Javascript can interact with HTML source code, enabling Web authors to spice up their sites with dynamic content. JavaScript is endorsed by a number of software companies and is an open language that anyone can use without purchasing a license. It is supported by recent browsers from Netscape and Microsoft, though Internet Explorer supports only a subset, which Microsoft calls Jscript.

Javascript is not Java. Javascript was influenced by Java. 

Java is a programming language and may be used for umpteen things, including games. It allows cross-platform compatibility. The fact that the games may appear at a website does not mean Java was used to build the site. 

Javascript is a scripting language. It's most common use is in web page design. Many "links" now are not simple HTML links, but use Javascript to call up content. That can add some enhancements. It can also be used as a method of hiding the location of a video to prevent downloads. Javascript can also be used in PDF documents and desktop widgets (renamed "Gadgets" by Microsoft to avoid appearing a copy of Apple's Widgets). 

In summary: Your browser properties / preferences allow on-off selection of both. If you turn off Java, nothing much happens until you go to a site that has applications available that should play online. If you turn off Javascript, most sites will have limited functionality (content does not appear in the page, or links do not work), as most sites nowadays are deeply embedded with Javascript. If you do not play online games, turn off Java. To prevent malicious connections via Javascript, use "NoScript" in Firefox.