A Lawson style sofa/couch has loose backing and cushions (allowing for more body conformity and comfort) and low, curved armrests.
A sectional sofa is broken up into several sections that you can combine to form one piece of furniture or use each piece separately. When put together, a sectional typically forms a curved shape.
A recliner is a chair (and sometimes one portion of a sectional) that has a mechanism that allows you to recline. There are often three recline levels: upright, with feet up, and fully reclined. Reclining is usually manual by use of a hand lever, but more expensive models have an electric, touch-button feature.
A chaise lounge is a sofa/couch with only one arm and a back across only half of the cushion, allowing for a relaxed sitting position with the feet up.
A loveseat is a small couch/sofa that only seats two individuals comfortably.