baby doctor vs paediatrician

baby doctor and paediatrician both are nouns.

Word	Noun	Adjective	Verb	Adverb
baby doctor	Yes	No	No	No
paediatrician	Yes	No	No	No

As nouns, baby doctor and paediatrician are synonyms defined as:

Other synonyms of baby doctor include pediatrician, pediatrist.

baby doctor (noun)	paediatrician (noun)
a specialist in the care of babies	a specialist in the care of babies