Are edema and swelling synonymous?

Basically yes: Edema is swelling caused by excess fluid trapped in your body's tissues. Although edema can affect any part of your body, it's most commonly noticed in the hands, arms, feet, ankles and legs.

Not always: In most instances when a patient says legs are swollen they are often are referring to edema, which is the accumulation of fluid in the extremities. However other things besides edema can cause swelling such as infection involving a body part, blood clots in veins(phlebitis), a bruise to the head or face, etc.