I’ve been trying to explain the difference between these two things (design and art) for, oh, about 20 years, but Joshua Porter does it way better and more simply than anyone else I’ve seen. The differences are perhaps not as stark as Porter desires but his point, that design is about usability and art is about expression (political, social, psychic), rings.
In case you’re skeptical, here’s the firstmost of his Five Principles to Design By (and I really recommend reading the rest):

Technology Serves Humans.
Too often people blame themselves for the shortcomings of technology. When their computer crashes, they say “I must have done something dumb”. If a web site is poorly designed, they say “I must be stupid. I can’t find it”. They might even turn to a book for Dummies to get it right.
This is horrible! People should never feel like a failure when using technology. Like the customer, the user is always right. If software crashes, it is the software designer’s fault. If someone can’t find something on a web site, it is the web designer’s fault. This doesn’t mean that the designer has to hang their head in shame…they should see this as a learning opportunity! The big difference between good and bad designers is how they handle people struggling with their design.
Technology serves humans. Humans do not serve technology.