skin disorder vs disease of the skin

skin disorder and disease of the skin both are nouns.

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

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

Other synonyms of skin disorder include skin disease.

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