The "OS" is the most rudimentary interface between the hardware and an end user. Like many things, there is a gray area at exactly where it begins and ends, but a Linux OS would include the kernel, a console, and arguably things like the X-windows core system and libc6 ... no more.
Desktop environments, and their associated applications constitute a subjective core of higher level tools to make the OS more usable for the average person. In the Linux environment, those "collections" of higher level tools are referred to as "distributions," or, in your case the system. I would prefer the term "environment" to "system."