jucheck is installed in program files (x86) by default, in either 64 or 32Bit.
You, or the person who installed Java, must have installed , automatically, the 64Bit Java.
By default, again, this would automatically go into "Program files" which is specifically for 64Bit programs.
Again, by default, it is placed in system 32. This is because System32 is where, on startup, windows looks for automatically loaded files.
WoW64 stands for "Windows on 64-bit Windows", and it contains all the 32-bit binary files required for compatibility, which run on top of the 64 bit Windows. The file in there is the 32Bit exe.
Fwiw. The file concerned with this thread, depending on how you use your computer, is not essential in startup. It is the periodic update file for Java. If you are content to manually update java from time to time, as I do, you can open Msconfig and, under the startup tab, untick it.