What is the difference between "Sofa" and "Couch"?

They are effectively interchangeable in the US.

A Google ngram of the terms shows that in the US, couch was slightly more common until the middle of the 19th century, and the usage has been almost equal since then, with a very slight favoring of couch.

The ngram for British usage shows a similar pattern with equal usage kicking in about 1930 and a slight favoring of sofa currently.

Searches of the websites of two major US retailers of furniture (Macy's and Pottery Barn) for sofa and couch yield identical results in the number of hits, but the text describing the products tend to use sofa.

Though the two words are usually used interchangeably in everyday speech, there is a slight difference. Couches are typically armless, while sofas are not, and the distinction comes from their respective historical uses. Depending on the attributes of the furniture that you are referring to, it could either be a couch or a sofa.

If you'd like, you can refer to http://www.homedit.com/what%E2%80%99s-the-difference-between-sofa-and-couch/ for more information.