Unix is popular operating system, developed by AT&T in 1969 and it has been very important to the development of the Internet. It is a multi-processing, multi-user, family of operating systems that run on a variety of architechtures. UNIX allows more than one user to access a computer system at the same time.
A widely used Open Source Unix-like operating system kernel. Linux was first released by its inventor Linus Torvalds in 1991. Combining the Linux kernel with the GNU software forms the basis of the operating system family generally known as ‘Linux‘. There are distributions of GNU/Linux for almost every available type of computer hardware from desktop machines to IBM mainframes. The inner workings of GNU/Linux are open and available for anyone to examine and change as long as they make their changes available to the public, as set out in the terms of the GNU General Public License. Because of its robustness and availability, Linux has won popularity in the Open Source community as well as among commercial application developers.
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• Unix requires a more powerful hardware configuration. It will work in large mainframe computers but will not work in an x86 based personal computer. Linux however, (which is built on the concept of Unix) has small hardware requirements and it will work on both a large mainframe computer and an x86 based personal computer.

• Unix is an Operating System developed in olden days in which the kernel, the heart of the OS, interacts directly with the hardware. (note: this is the definition of what a kernel is). Because UNIX treats everything as a file, it provides greater security for users. An example of a UNIX distribution is posix. (note: actually POSIX is a set of standards for interoperability of applications between UNIX and UNIX-like systems). Linux uses a the UNIX architecture as its basis and provides more facilities and applications. Linux could be considered to be a GUI to the UNIX core. (note: this is plain wrong. GNU/ Linux was rewritten from scratch using UNIX as a guide. GNOME and KDE are GUIs for GNU/Linux). Examples of Linux distributions are Redhat, Fedora, Susee, Mandriva, and Ubuntu. Solaris OS also uses the UNIX kernal almost all UNIX commands will work on solaris in addition to 500 Solaris specific commands. (note: Solaris is also a rewrite of UNIX for x86, and does not use any original UNIX code). Both UNIX and LINUX are Open source. (note: UNIX is proprietary, Linux is open source)

• Unix is the foundation for a number of operating systems, with Linux being the most popular one. Novell and Free BSD are 2 other commonly used Unix varients.(note: Again, the BSD family are based on another rewrite of UNIX for x86, UNIX is not their foundation in the sense implied here)

• UNIX is an operating system created in the early days of computers. More recently, Linux was created as an open-source, freeware operating system. (note: Linux is free software, not freeware. Free software is open source that insists any developer reusing code releases their own work as free software. Freeware is proprietary software distributed at no cost [gratis]) It is “UNIX-LIKE”, meaning that it uses many UNIX constructs but also departs from traditional UNIX in many ways. Like UNIX, Linux is faster than many of the other commercially available operating systems. (note: This is a sweeping generalization and depends on the hardware used, and what servers and applications are running) It appears to also be far more robust than any of the Microsoft products. Linux is being used in many time critical applications because of it’s speed. It is also used in many applications that need to maintain uptime because Linux, like UNIX, can run for months at a time without rebooting. While the typical method of solving Microsoft problems is to “reboot”, that particular requirement does not seem to be appropriate in a Linux/Unix environment. While UNIX has created a windows-like work environment, Linux has improved greatly on that concept. Linux has become a real player in the consumer operating system market… and it’s free. While you may want to pay for a Linux distribution, the actual code is free and you are allowed to load it on as many machines as you want. You can get Linux for free if you wish to load it across the internet. 

Some other way to express difference 


Unix :

A Operating System developed in olden days in which kernel interacts directly with the hardware.kernal is consider to be heart of this os.
In this Operating system everything is considered as a file,provides greater security.
Ex: posix

Linux :

Linux is an Operating system which use unix as its base and gives further more facilities and applications.
Merely speeking GUI is made in linux having unix as its core.
Ex: Redhat, Fedora, Susee, Mandrake . . .
Solaris OS also using the same unix kernal all the unix commands will work on solaris and have 500 more solaris specific commands. Differnent organizations used the UNIX kernal and added their own essence to form their own version of linux.
Both UNIX and LINUX are Open source