**Art** is typically something that an artist designates as art, or society has deemed culturally important. It’s often a physical work (or just an idea) that had a certain aesthetic or intellectual intent. It’s purpose can vary, from being an outlet of personal expression, to excite the eyes, to set a mood/emotion, to provide commentary, etc.

**Design** is typically meant to give order to an idea or goal, to address problems, and solve them. Designers have to deal with practical utility (something that serves a purpose). What sets designers apart is that they must consider function and usefulness in addition to artistic qualities. However, some designers may have no interest or skill in art and deal strictly with researching or conceptualizing ways to manage an issue through design.

##They can overlap heavily.
More confusingly, Applied arts deals with the use of art for a specific purpose.Industrial design, graphic design, fashion design, interior design and the decorative arts can be considered applied arts as well as design practices.

Something like architecture involves a sense of visual art and necessity for careful design.

Commercial illustrator artists create art with design purpose for a business (like a cover of a magazine). 

Some designers can make work that does the job for design, but also is a work of art. 

I’m sure a handful of objects in history museums were both design and art. A pot was meant to hold water/food/plants (design), while the shape or visuals also provided snapshot of the culture (art).

##One difference is practicality.

Art does not need to be practical whereas design does. A chair that will be used needs to be designed for the proper purpose (to sit on it). And a chair can be art because it is designated (like a readymade). A person could also make a chair made of sharp spikes and it could be art, but not really the right design for sitting.

In reference to the comment below, design can have no final practical outcome (such as a wallpaper designer). However, a wallpaper designer still has to consider practicality within a highly decorative medium. They probably have intent to comply within certain parameters: such as how the form or pattern may repeat and seamlessness of each strip, what scale make sense for a wall to be visible in a room, the appropriate subject matter (or abstraction) that is suitable in a household or business. They may also think of what is practical from a business perspective (Does this design have enough appeal to be profitable?). Wallpaper isn't usually considered "fine" art, but the wallpaper designer may feel that the design requires forms of art, whether subtle, simplistic, or bold to contrast with the interior space.

To sum up, artists aren't confined by practical restrictions (although sometimes they can be self-imposed). Designers may be required to create under certain guidelines that may or may not have artistic components.