Artist vs. Inventor

What is the difference between an artist and an inventor?  Some people clearly fall into one category or the other, but it is difficult to put others into just one category.  A person who is purely an artist creates something from materials already available to them.  They copy from either nature or their mind.  An inventor also uses materials already available to them, but they create something with a new purpose.  An inventor creates a new method to complete a task.  Inventors also find a solution to a physical problem whereas this does not really apply to artists.  Artists and inventors share many characteristics.  They both use what they have to create something unique.  Many artists are partly inventors by developing new methods to create their art and many inventors are artists in using their creativity.  In that sense, no one is just an 'artist' or just an 'inventor'.