Linux is Unix.
Linux is not a licensee of the UNIX trademark.
Much depends on how you use the term Unix. You may mean the UNIX trademark, which is held by the "Open Group" http://www.opengroup.org
. The trademark holders and those who have licensed it would prefer that you never use "UNIX" to refer to anything other than products sold by companies who have licensed the "UNIX" trademark, and that you never use the terms "Unix" or "unix" at all.
If you are the sort of person who likes to bend over for US industry groups and corporations and let them control the language you use, then by all means, you are free to use the term UNIX in this way. You might be the sort of person who can say "Kleenex(tm) brand facial tissues" with a straight face. You should also note that POSIX is itself a trademark, one which no GNU/Linux distribution is licensed to use.
I use "Unix" in a more historically accurate way, because I choose to be true to history, to the community, and to language rather than to bow to the wishes of an industry trade group. "Unix" is a term with a long history, and refers primarily to an interface, both the command-line interface presented to the user, and the system call interface defined by C header files and presented to programs. This is what I, and most of the world, mean by "Unix" or "unix" and I would encourage you to use these terms as well when referring to these interfaces or to software implementations (such as GNU) that provide these interfaces. By this historical definition, GNU clearly *is* Unix, and the modern GNU/Linux operating systems are Unix as well. FreeBSD, OpenBSD, and NetBSD are also Unix by this definition, and I feel free to refer to them as such. Mac OS X runs on Darwin, and Darwin is Unix too.
Personally, I reserve "UNIX" in all-caps to refer to the trademark itself and the closed, proprietary UNIX variants such as HP-UX, SCO UnixWare, and Solaris, which license that trademark. I consider these products obsolete (and based on industry sales figures, so does most everyone else), and so I seldom have a need to refer to them as a group, but if I ever did, I might say something like "the obsolete UNIX variants." Generally I never write anything in all-caps anyway, so I'm willing to reserve "UNIX" to refer to this dead industry segment.
However, I am not willing to allow these companies to control how I use such a fundamental term in the vocabulary of computers as "Unix" or "the unix user interface". "Unix" is too useful and describes too much history to let it die with the likes of SCO.
I hope this clears some things up for you regarding terminology, and I hope even more that you'll join me in refusing to let an industry trade group control our language.