Whereas most OS programmers refer to Linux-OS as Linux and the kernel as the Linux Kernel for a good reason, they are entirely separate projects. There are many different Linux Operating systems, there is only one legitimate Linux Kernel. Even security enhanced linux uses the Linux Kernel.
After I said that I went straight to Wikipedia to back up my statement, and noticed it wasnt word-for-word equivalent, but I kept it anyway, because I usually consider Linux to just be the kernel, and when referring to it as an OS I say Linux-based OSs.
vBulletin is not open source in the traditional sense, that is it is not in the public domain, only licensed customers have access to the source code, which is a necessity as its written in php.
Also, I would suggest not to use Wikipedia because its open-source and Ive read every line of its source and its spaghetti code. Also, I would stay away from this website because it uses free and open-source software with terrible code, too.