There's a long debate on what is "UNIX" or Traditional UNIX. You need to be aware of the UNIX history. In today's world UNIX is a trademark and represents a bunch of OSes which maintain a certain standard. AIX, HP-UX, Solaris, *BSDs code bases were derived from UNIX SYS V R4 and Berkley UNIX (for *BSDs). Whereas Linux was written from the scratch, but it behaves like one of the UNIX systems. When people say UNIX they actually mean AIX, HP-UX, Solaris or *BSDs. Linux is UNIX like OS. But that does not make Linux any less UNIX in behavior than the other OSes mentioned.
Also, there is POSIX standard which provides single UNIX specification. AIX, Solaris, HP-UX, Linux and even *BSDs conform to the POSIX standard to some extent and diverts from it when needed.
Wikipedia will give you a good overview on UNIX and POSIX
Unix - Wikipedia, the free encyclopedia
POSIX - Wikipedia, the free encyclopedia