higher education vs education

higher education and education both are nouns.

Word	Noun	Adjective	Verb	Adverb
higher education	Yes	No	No	No
education	Yes	No	No	No

As nouns, education is a hypernym of higher education; that is, education is a word with a broader meaning than higher education:

higher education: education provided by a college or university
education: the activities of educating or instructing; activities that impart knowledge or skill

Other hypernyms of higher education include didactics, educational activity, instruction, pedagogy, teaching.

higher education (noun)	education (noun)
education provided by a college or university	the activities of educating or instructing; activities that impart knowledge or skill
	the profession of teaching (especially at a school or college or university)
	the result of good upbringing (especially knowledge of correct social behavior)
	knowledge acquired by learning and instruction
	the gradual process of acquiring knowledge