The second major difference between Linux and UNIX is how they are licensed. GNU/Linux is licensed under the GPL (GNU General Public License) which is an open source license. This means that the code for the kernel is available for anyone to use or change, as long as the changes are also licensed under the GPL.
UNIX, on the other hand, is traditionally a commercial product with a proprietary license. The UNIX trademark is held by The Open Group which is an industry standards consortium. The Open Group only allows operating systems that are fully compliant with the Single UNIX Specification, and are certified as such, to use the UNIX name. I say traditionally because Sun recently released OpenSolaris which is licensed under the Common Development AND Distribution License (CDDL) which is an open source license.