Craft
A craft or trade is a pastime or a profession that requires particular skills and knowledge of skilled work. In a historical sense, particularly the Middle Ages and earlier, the term is usually applied to people occupied in small-scale production of goods, or their maintenance, for example by tinkers. The traditional terms craftsman and craftswoman are nowadays often replaced by artisan and rarely by craftsperson (craftspeople).
Design
Design is the creation of a plan or convention for the construction of an object, system or measurable human interaction (as in architectural blueprints, engineering drawings, business processes, circuit diagrams, and sewing patterns). Design has different connotations in different fields (see design disciplines below). In some cases, the direct construction of an object (as in pottery, engineering, management, coding, and graphic design) is also considered to use design thinking.
Design
People think it's this veneer — that the designers are handed this box and told, 'Make it look good!' That's not what we think design is. It's not just what it looks like and feels like. Design is how it works.
Steve Jobs (2003), as quoted in Rob Walker, "The Guts of a New Machine", The New York Times Magazine, 30 November 2003