Craftsman manufactures garage door openers under their name (Sears Craftsman) as well as Liftmaster and Elite. There is no difference between Craftsman and Liftmaster other than branding and where the models are sold. I have found that is is often cheaper to buy the Sears Craftsman openers and Liftmaster remotes and accessories such as the photoeyes, remotes, and/or keypads. In terms of models, that all depends on preference. Chain drives are the most common and cheapest. However, they are much louder than belt drives. Source(s):