disease of the skin vs skin disorder

disease of the skin and skin disorder both are nouns.

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

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

Other synonyms of disease of the skin include skin disease.

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