If the guy down the street shows you how to play the guitar and helps you develop a masterful plucking style, then he's your guitar teacher.
A teacher is anyone who teaches things. Schools hire people to be teachers, but you don't have to work in a school to be a teacher. You can be a teacher to your children. If you're really good at making pizza, you can be a teacher to an aspiring pizza chef. If you're really passionate about methods of education, then you can become a teacher who teaches teachers how to teach better. Whoa.