先生 implies a teacher with a certain amount of respect. 教師 also means a teacher, but more focusing to simply express profession. We will not call someone like "Katia 教師". We will use the expression "Katia　先生"

Hola Katia, We use 先生 not only for teachers, but also, for example, doctors, layers, martial ars masters and so on. "先生" has more respect as Takashi-san wrote, and it is as written "somebody who was born earlier", which is the idea to respect elderies from religion. "教師" is just one of professions to describe what they do for living.