물고기 refers to live fish. 생선 is the fish meat for eating.

Google translate says this is the right word for fish

Not when you are talking about the animal. 물고기, is used for the flesh of the fish and is literally "the meat of the water" :)

선생님 = teacher, 생선 = fish

생선 vs 선생 :-)

Lol. Not quite. Teacher is 선생님. 생선 is fish.