What is the difference between rosacea and eczematous dry skin?

Everything.: The two have virtually nothing in common, actually. Rosacea is periodic flushing, dilated blood vessels, and (usually) acne-like papules on the face. Eczema is a term used to describe any number of dry, itchy rashes anywhere on the body.

Rosacea: Rosacea is red pimples and eczema is red, itchy , dry skin.

Rosacea & eczema: There are several excellent answers on the differences between rosacea and eczema. I would like to add one condition that is rosacea but can look like eczema. That is perioral dermatitis. Perioral dermatitis can be red, itchy, scaly and can definitely be mistaken for eczema. However, treating it like eczema with moisturizers and steroid creams can actually make it significantly worse.