eczema vs skin disease

eczema and skin disease both are nouns.

Word	Noun	Adjective	Verb	Adverb
eczema	Yes	No	No	No
skin disease	Yes	No	No	No

As nouns, skin disease is a hypernym of eczema; that is, skin disease is a word with a broader meaning than eczema:

eczema: generic term for inflammatory conditions of the skin; particularly with vesiculation in the acute stages
skin disease: a disease affecting the skin

Other hypernyms of eczema include disease of the skin, skin disorder.

eczema (noun)	skin disease (noun)
generic term for inflammatory conditions of the skin; particularly with vesiculation in the acute stages	a disease affecting the skin