Extracted from http://www.homeinstitute.com

There are several different ways to categorize sofas. One way is by the style. Here are some of the most frequently found styles of sofa:

Chaise Lounge—a sofa that has a backrest at one end and no arms (also a reclining chair).
Chesterfield—a sofa with padded arms and a back that are the same height and which curve outwards at the top.
Chippendale—the style of sofa designed by Thomas Chippendale, an eighteenth century English furniture maker.
Davenport—a large upholstered sofa.
Divan—a long, low sofa with no back or arms, often set against a wall with a backing of pillows.
Love Seat—a short sofa for only two people; it can also describe a sofa shaped like an S, so that two people sitting on it can face each other.
Sectional Sofa—a set of sections of sofa that can be configured as the homeowner desires, most typically in an "L" shape.
Sofa Bed—a multifunction sofa that folds out into a sleeping platform with a built-in mattress.

Another way to group sofas is by the number of people they are meant to seat.

One person—chaise lounge, divan
Two people—loveseat
Three people—(usually) chesterfield, chippendale, davenport, sofa bed
Many people—sectional sofa

Upholstery

Sofas can be upholstered in a wide variety of materials:

Plant Fibers—cotton (including denim) and linen
Animal Fibers—silk and wool
Animal Hide—leather
Synthetic Fiber—including acetates, acrylics, nylon, polyester, polypropylene (Olefin), and vinyl (Naugahyde).

Construction

A sofa is comprised of four basic parts: the frame (which gives it form and is often made of hardwood); the springs (which supply support); the padding, which creates a zone between the springs and the upholstery material; and the upholstery itself. A fifth element, cushions, may or may not be part of a couch, and is created from fill covered with upholstery.