The Java Runtime Environment (JRE) provides the libraries, the Java Virtual Machine, and other components to run applets and applications written in the Java programming language. In addition, two key deployment technologies are part of the JRE: Java Plug-in, which enables applets to run in popular browsers; and Java Web Start, which deploys standalone applications over a network. Users should install the 32-bit version if they are using 32-bit browsers. If you use both 32-bit and 64-bit browser interchangeably, you need a Java Plug-in for each browser. Hence you will need to install both 32-bit and 64-bit Java respectively.
Thanks to Astron for the update.