From a practical POV, the main difference between the terms Unix and Linux is that the former describes a wider family of operating systems, while the latter describes a more specific subgroup.
For all practical purposes (thus ignoring RMS, technical accuracy, trademarks and other legal aspects), the term Linux applies to a number of operating systems, known as distributions: e.g. Red Hat, Fedora, Ubuntu, Debian and so on.
Unix (again, blatantly ignoring technical accuracy, trademarks and other legal aspects) is a wider family of operating systems to which Linux belongs. Thus, we could say that all Linux distributions are part of the Unix family. But people have come to use the term Unix to mean Unix operating systems other than Linux. Examples of Unix that are not Linux include OS X, FreeBSD, and Solaris.
Asking for the differences between Unix and Linux is like asking for the differences between Mammals and Dogs.
All dogs are mammals, but one could say that they are generally more suited for being pets than other mammals. That does not mean that other mammals like cats can't be excellent pets.
In the same way, it would be ok to say that generally speaking Linux is less expensive than Unix (that does not exclude the existence of expensive Linux or free Unix distributions)
If you want to compare one operating system to another you will have too be more specific, cause otherwise the terms are to vague to make a clear comparison.