eczema vs disease of the skin

eczema and disease of the skin both are nouns.

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

As nouns, disease of the skin is a hypernym of eczema; that is, disease of the skin 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
disease of the skin: a disease affecting the skin

Other hypernyms of eczema include skin disease, skin disorder.

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