Building on top of what everyone else has said, for a long time there were two kinds of UNIX: sysv5 which grew out of the original UNIX developed by Bell labs, and BSD which grew out of Berkeley.
Your big commercial unixes like SunOS and Irix were based on sysv5. There were smaller commercial offerings like BSD/OS from BSD that had a much nicer userland.
Linux more closely followed the sysv5 model, but the gnu user land had a lot of the niceties of BSD.
There is also something called POSIX which is a set of standards that describe what it means to be UNIX. While UNIX is a specific commercial code base that licenses out its code to other companies to build whole OSes, POSIX publishes specification for developers to follow.
Happy hacking!
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