It is a real jar. I don't know what is a fake jar, anyway...
Example: I exported a sketch named Hearts with Processing 1.5.1. I got an application.windows folder (I don't need the other modes). Inside, there is Hearts.exe, which I can ignore now. And two folders: source, with textual files, and lib. In the later, I have a Hearts.jar, a core.jar (Processing itself) and a text file with command line arguments in it. You can have more files if you used libraries, files, etc.
If I open a command line in the lib folder, I just type
java -cp Hearts.jar;core.jar Hearts and I have my sketch launched. This line can work almost on any system (on Linux, you have to replace the semi-colon with a colon). Here, you have a portable application (as long as Java is installed on the system, and the java exe is on the path).
Bonus: with your favorite archive manager, unzip both jars. Yes, they are just plain zip files. Start with core.jar, then Hearts.jar (or whatever you named it). You will probably be asked if you want to overwrite MANIFEST.MF. Say yes.
You end with some .class files (or only one for a simple sketch), a META-INF folder and a processing one. Select them, then zip them back.
I use 7-Zip, I can select the jar in the Windows Explorer and in the context menu, I can choose 7-Zip > Extract Here twice, then on the said files, 7-Zip > Add to "lib.zip".
I renamed the resulting file to ProcessingHearts.jar, for example.
I can then run it with:
java -jar ProcessingHearts.jar
Only one jar, the same command line to launch it on all systems, all is nice!