Both are different operating systems:
1. Linux is just a kernel. Linux includes GUI system + GNU utilities +installation
& management tools + GNU c/c++ Compilers + Editors (vi) + and various applications.
UNIX is a complete operating system as everything come from a single source.
2. Linux is free version But Unix is not.
3. Linux use ext3 or ext4 as file systems.
UNIX have various file systems such as jfs, gpfs (AIX), jfs,etc.