Historically, the term "couch" actually referred to a piece of furniture similar to a chaise, designed for one person to lounge on. These couches usually had one arm and a tapered back. The word sofa, on the other hand, came from the Arabic word "suffah," which was used to describe a bench covered with cushions and blankets.
While most couches are designed to seat three people comfortably, sofas usually have room for four. Sofas are also likely to come equipped with a pull-out bed.
Because of the difference in size and function, sofas are usually somewhat more expensive than couches. They are also heavier and more difficult to move, but they provide the convenience of a place to sleep for overnight guests.