I have seen the two words being used over and over again here but don't know whether they are synonyms of each other or not. The Usage guides for the two tags seem not to help very much:
Travel with children of all ages from infants to toddlers to teenagers.
Questions about people younger than the age of adulthood, generally younger than 18 to 20 years old.
Can somebody elaborate about the 'age' part?
Created by the same user, presumably some difference was intended.
Selecting for Google's preferred definition sets:
child: a young human being below the age of puberty or below the legal age of majority.
minor: a person under the age of full legal responsibility.