Essentially they are the same thing, with 'couch' being a more popular term in the United States. It comes from the French word 'coucher', which means 'to sleep'.
'Sofa' is a more popular term in British English, most commonly used in the United Kingdom and India. Origins of the word is thought to come from the Arabic word 'soffah', a raised part of the floor for sitting and covered with cushions and carpets.