Eczema is the name for a group of skin conditions. There are different symptoms for each type.
Dry skin is a trigger for eczema, which is also called atopic dermatitis. And eczema is one possible cause of dry skin.
Atopic dermatitis and contact dermatitis can have similar symptoms, but different causes and triggers.
Weeping eczema is a problem that stems from eczema where your skin oozes clear or straw-colored liquid.