One way to look at these concepts. (From my innovation workshop at BYU)
Art is very novel and not very useful.
Innovation is very useful and not very novel. This is where design efforts should be focused.
Invention is very useful and very novel. Examples include the light bulb, the Model-T, and the first Macintosh. True invention is extremely rare.
Science is like art. It is usually very novel and not very useful. Science becomes useful when applied in an invention or innovation.