I dont agree that cellulitis and erisypelas are synonymous, I think there are some real, albeit small/subtle distinctions between them.
Cellulitis is infection of the underling fat tissue, it has a nondistinct, hazy border. Erisypelas is an infection of the lower layers of dermis (above the fat tissue level) and has a much sharper area of demarcation. Erisypelas is classically caused by strep, cellulitis can be caused by several organisms including strep.
Abscess is a localized, separated compartment of pus than can exist in any layer of skin or any other organ. Most common cause is staph for skin abscesses.
Interestingly several studies have shown that I&D by itself may be sufficient to treat many skin abscesses and that antibiotics may not be necessary. However, in clinical practice the de facto "standard" is still I&D + oral abx.