I do believe the teacher can make a difference, but the same teacher will not make the same difference to every student. The thing to seek is the good relationship, or the good match between student and teacher, since not every student learns in the same way, nor seeks the same outcome.
Thus I found the study mentioned by Moonbear completely in line with what I have observed over my career, When I read teacher evaluations of professors in order to give awards or promotions, I observed that overwhelmingly, the highest evaluations went to the professors who gave the highest grades. Those professors apparently had the happiest students. In some cases those professors were also excellent at explaining the material, but they tested that material in a far less challenging way than others did. In those cases their grades did not discriminate at all between merely average good students and really excellent ones as essentially everyone got an A.
There were also exceptions however. There were some professors who were both challenging and excellent and this was noted by the students who said the professor's class was not easy but they felt the professor went out of her/his way to give the students every chance to learn as much as possible. When awarding prizes for teaching I looked for these latter instances, but they were only a small subset of the teachers.
Indeed since promotions and raises and hiring depend in many cases at least partly on these evaluations, most teachers have apparently learned to placate the students with easier classes, and not to make the grade depend on really excellent performance.
So as Moonbear made clear, the meaning of the term "good teacher" depends on what the evaluator is looking for: clear explanations, deep insight, more advanced versions of material than found in books, higher grades than average or than deserved, willingness to overlook lazy performance or absences, concern for the student's needs and feelings,....
Years ago I wrote an essay "On teaching" that was published by request of one of my students then in the math ed department. It is #8 under class notes on this page:
In it I refer to the passage in scripture where Jesus rebukes a follower for calling him "good teacher", responding none is actually good except God.