General term for a teacher, especially in a school setting. Can also refer to instructors in other contexts.
He is a high school math teacher.
良い教師は生徒のやる気を引き出す。
A good teacher brings out students' motivation.
She says she wants to become a teacher in the future.
He has worked as a teacher at a high school for ten years.
She is studying education at university, aiming to become a teacher.
I was taught Japanese by that teacher.
教師 is the general word for a teacher, usually in a school, while 家庭教師 specifically means a private tutor who teaches one-on-one, often at home.
教師 broadly means any teacher or instructor regardless of licensure, whereas 教諭 specifically denotes a certified teacher in an official capacity.
role of teacher; teacher role
ordained minister; regular teacher