dermatologist vs skin doctor

dermatologist and skin doctor both are nouns.

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

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

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

dermatologist (noun)	skin doctor (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