The term puffy eyes doesn't mean the same thing as swollen eyelids. The two terms refer to different conditions.Swollen eyelids, or swelling around the eyes, is an inflammatory response to allergies, infection or injury. Eyelid swelling can happen with just one eye or both eyes. Eye puffiness is usually related to lack of sleep, age-related sagging of tissue and general water retention. If you have puffy eyes, it will typically affect both eyes.