先生 and 教師: a form of address and a profession
Distinguish the title 先生 from the occupational noun 教師.
Addressing someone
先生 (せんせい) is a respectful term for teachers and certain other people. 「先生、質問があります」 directly tells a teacher that one has a question.
「田中先生に聞きました」 means asking Tanaka-sensei. 先生 follows the name as a title.
Describing a profession
教師 (きょうし) names the teaching profession. 「私は中学校の教師です」 introduces the speaker as a middle-school teacher.
「教師になりたいです」 expresses a wish to become a teacher. Distinguish this from having already become one.
The scope of use
Doctors may also be addressed as 先生. Hearing that title alone does not establish that someone teaches at a school.
Do not mechanically replace 先生 with 教師 when calling out 「先生、こちらを見てください」 at school. An occupational noun and direct address serve different roles.
If a doctor is called 先生, does that mean the doctor is a schoolteacher?
Show the answer and why
No. 先生 can address people other than teachers and does not establish the profession.