catechist vs teacher

catechist and teacher both are nouns.

Word	Noun	Adjective	Verb	Adverb
catechist	Yes	No	No	No
teacher	Yes	No	No	No

As nouns, teacher is a hypernym of catechist; that is, teacher is a word with a broader meaning than catechist:

catechist: one who instructs catechumens in preparation for baptism (especially one using a catechism)
teacher: a person whose occupation is teaching

Other hypernyms of catechist include instructor.

catechist (noun)	teacher (noun)
one who instructs catechumens in preparation for baptism (especially one using a catechism)	a personified abstraction that teaches
	a person whose occupation is teaching