This article answers all your questions about the spelling of these two words along with definitions, origins, usage and examples. Read along and you will get to know the difference between the two spellings.
Pediatric as a noun:
Pediatric is the branch of medicine that deals with the medical care of infants, children, and adolescents, and the age limit usually ranges from birth up to 18-21 years of age (in some places until completion of secondary education). A medical practitioner who specializes in this area is known as a pediatrician, or, a paediatrician.
Pediatric as an adjective:
Pediatric or paediatric:
Pediatric (without an a) is the spelling most commonly used in American English which was changed back in the 19th century, thanks to Noah Webster and his ‘theory of difference’. The original spelling of the word is 'paediatric' (with an a), which was first derived from the Greek language and is still used in all of the world except America.
This acute-care and community teaching hospital trains medical residents in many disciplines, including internal medicine, critical care medicine, surgery, pediatrics, podiatry, and pathology. [CNN Money]