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What's the difference between unix and linux?

Mostly, Linux is considered to be a copy of UNIX.Linux is an example of Open Source software development and Free Operating System.Unix is operating system, that is popular in universities, companies, big enterprises etc.

Linux can be freely distributed,downloaded freely, distributed through magazines, books etc. There are priced versions for Linux also.
Different flavours of Unix have different cost structures.

Unix OS were developed mainly for mainframes, servers and workstations.

Linux typically provides two GUIs,KDE and Gnome.But Linux GUI is optional.
Initially Unix was a command based OS, but later GUI was created called Common Desktop Environment