Please, delete the two other threads, thanks.

Answer: Java is, in general, system agnostic, indeed. But Processing comes with a few native libraries, ie. shared libraries on Unix systems, DLLs on Windows.
For example, the serial library, and more typically, the OpenGL library.

Although my copy of Processing for Windows includes both formats, probably for generation of standalone executables and perhaps the export applet option.

Another explanation is that Processing tried to tightly follow platform practices, so the Mac version is distributed as .dmg file, while the non-expert version of Windows is shipped with a version of the Windows JDK. Which is, itself, system dependent: although most of Java is written in Java, it still relies on a few core C native functions.
I think Linux and Mac versions are JDK-less as Java is generally installed out of the box on these system (on Mac, it is a version made by Apple).