Linux is a "free as in freedom" operating system kernel started by a Finnish college student in 1991. It has subsequently grown into one of the largest examples of free software on earth. When used colloquially Linux refers not only to the kernel itself but the whole operating system running on top of it. This most prominently includes the GNU toolset and libraries which are used by almost all applications running on Linux. And it also includes X.org, the underpinning of the graphical user interface that most users interact with, as well as KDE and Gnome -- the two major GUI toolkits, and a number of other components from various sources.
A "Linux distribution" is a collection of programs running on top of the free Linux kernel. A distribution generally includes programs and program libraries from thousands of sources. To keep all of this manageable, the community has settled on a limited set of standardized software licenses, the most popular being the GPL, MIT, and Apache families of licenses. But there are other licenses, both Open Source Initiative approved "free[dom preserving]" licenses that exist mostly due to historical artifact, and "free as in beer not freedom" licenses which have certain limitations (often on commercial use.)
LinuxMCE contains both "free as in freedom" components and "free as in beer" components. Except for a very few exceptions, which we try to keep to an absolute minimum, even the "free as in beer" components do come with source code which anyone can modify and experiment with.