Art is a way of outwardly expressing your emotions; with many different forms of media such as traditional art, music, acting, etc. Truthfully, the definition of art can vary from person to person. Painting, drawing, sculpting, crafting, would be classified under societies category of “The Arts.”
Design is another form of media that is art. Whether it is designing clothes or a graphic, design is a more literal use of art in the everyday (i.e. logos, brochures).
Craft is a larger umbrella of a category of art. Craft can be defined from sculpting to woodcutting to paper craft.