skin doctor vs dermatologist

skin doctor and dermatologist both are nouns.

Word	Noun	Adjective	Verb	Adverb
skin doctor	Yes	No	No	No
dermatologist	Yes	No	No	No

As nouns, skin doctor and dermatologist are synonyms defined as:

skin doctor and dermatologist: a doctor who specializes in the physiology and pathology of the skin

skin doctor (noun)	dermatologist (noun)
a doctor who specializes in the physiology and pathology of the skin	a doctor who specializes in the physiology and pathology of the skin