Traffic light: a signal that controls the traffic on a road, by means of red, orange and green lights that show when you must stop and when you can go Source
But many people say "stop light", but seem British means it "a red traffic light" & American means it "traffic light" or "brake light" (Source).
So, what is red traffic light?
But sometimes, people say "Go straight and then turn left at the light". So, "light" also means "traffic light"?
In short, the ones that are correct are all the same.
They all look like this:
As an American having lived in various parts of the country, I can safely say that "brake light" isn't used AT ALL for traffic lights. It means something very different in fact. It is the red light on the back of a car that lights up when you brake that looks like this:
Of all of the words you gave, traffic light is the most common. Stop light is also used sometimes. I'm guessing that red traffic light came along as a synonym for stop light, because the light is red. It is the same thing as a traffic light.
Take a look at the Ngram for those terms to see for yourself:
In the context of giving directions, yes, "light" implies a traffic light, unless there is some other landmark around like a HUGE lightbulb. But that isn't usually the case.
In American English, "traffic light", "stop light", and "the light" (as in "turn right at the light") are all used to mean the same traffic control signal.
Most of the time "break light" (or rather, "brake light") refers to the red light on the back of a car that indicates when the car is stopping.
