FreeBSD http://www.freebsd.org/ is a very solid version of Linux based on BSD Unix, which is descended from AT&T UNIX via the Berkeley Software Distribution (BSD). And BSD is used as the foundation for other operating systems like Apple OS X and FreeNAS. This is well tested and updated frequently, known for its tight security, reliability, robustness and stability. BSD is a hybrid - it is not fully Unix and it is not fully Linux; but it is compatible with both. I highly recommend it.
It is NOT linux, and though it can be made to run linux binaries, it does not do so without some tweaking. And yes, because of its structure, it can be called Unix. The distinction is that the name Unix is trademarked, having been owned by AT&T's Bell Labs, then Novell (remember Unixware?), and now ??? It has been sold a few times, and that product, with the source code from the original AT&T product, is the only thing that can truly be trademarked as Unix. Technically BSD was never called BSD Unix, for the reason above. FreeBSD was the continuation of BSD 4.4 after its development ended.