It seems they are all the same.
SOFA. an upholstered seat for more than one person
SETTEE, A long seat or bench with a back and arms seating two or more people.
COUCH, also known as a sofa, settee, or chesterfield is an item of furniture for the comfortable seating of more than one person.
Here in my part of the U.S., sofa and couch are used almost interchangeably. (Settee is something found in antique shops.)
The main difference between sofa and couch seems to be dollars spent. But couch, not sofa, is the cheaper item - most likely to be left by the side of the road once the springs sag. Sofa implies big bucks and the promise of reupholstery once the fabric trends change. Of course, I own naught but sofas.