What is the difference between fashion design and graphic design?

Not much. Graphic design is the creation communicative material, typically for print but can also for the web, such as logo design, editorial layouts, business card designs, brochure, flyers, and other promotional material, book covers/interiors, album artwork etc.

Fashion design is the design of clothing garments and accessories and can also involve the creation of repeating patterns for printing onto material.

Occasionally the line between the two may blur, for example on typographic t-shirt designs, but generally the two are very different mediums.