preterm baby vs premature infant

preterm baby and premature infant both are nouns.

Word	Noun	Adjective	Verb	Adverb
preterm baby	Yes	No	No	No
premature infant	Yes	No	No	No

As nouns, preterm baby and premature infant are synonyms defined as:

preterm baby and premature infant: an infant that is born prior to 37 weeks of gestation

Other synonyms of preterm baby include preemie, premature baby, premie, preterm infant.

preterm baby (noun)	premature infant (noun)
an infant that is born prior to 37 weeks of gestation	an infant that is born prior to 37 weeks of gestation