infant school vs grammar school

infant school and grammar school both are nouns.

Word	Noun	Adjective	Verb	Adverb
infant school	Yes	No	No	No
grammar school	Yes	No	No	No

As nouns, grammar school is a hypernym of infant school; that is, grammar school is a word with a broader meaning than infant school:

infant school: British school for children aged 5-7
grammar school: a school for young children; usually the first 6 or 8 grades

Other hypernyms of infant school include elementary school, grade school, primary school.

infant school (noun)	grammar school (noun)
British school for children aged 5-7	a school for young children; usually the first 6 or 8 grades
	a secondary school emphasizing Latin and Greek in preparation for college