There are separate 32 and 64 bit Java Runtime Environment installers. See http://www.oracle.com/technetwork/java/javase/downloads/jre7-downloads-1880261.html. Adobe Flash installers include the 32 and 64 bit versions.

I have both installed Java 32 and 64 on my laptop. The one needed is dependent on the software that is calling the Java function, not just the OS.