skin disease vs disease of the skin

skin disease and disease of the skin both are nouns.

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

As nouns, skin disease and disease of the skin are synonyms defined as:

Other synonyms of skin disease include skin disorder.

skin disease (noun)	disease of the skin (noun)
a disease affecting the skin	a disease affecting the skin