What are the differences between Unix and Linux?

I’m confused about Unix and Linux. What is the Unix OS that we can install on my PC?

Unix was a widely influential operating system to come out of Bell Labs in 1969. You won’t be able to install that OS on a modern PC (even finding original copies of the code is becoming exceedingly hard). Unix went on to influence a wide range of other operating systems, many of which are still in use today. Linux is a modern OS whose design was inspired by Unix (however as I understand it, the Linux codebase did not directly descend from the original Unix codebase).

There’s a short description of how Unix relates to other operating systems, including Linux, on wikipedia. More about the early history of Unix can be found in this article.