Why have the speaker used "be" instead of "have" in the following sentence? "Stars are not the same brightness." I am confused because it seems to me that the word "brightness" has been used there as an adjective. What if the speaker had used "have", for example, " Stars don't have the same brightness", would it mean the same? If not, what is the difference then?
You are correct. The given sentence is not good English.
Stars are not equally bright or Stars do not have equal brightness are both grammatical ways to express the intended thought (though both offend my sense of good English style).
It is possible that the sentence quoted contains a typographical error and should have read:
Stars are not of the same brightness
The addition of "of" makes the sentence grammatical although again it seems poor style to me.
How would I have expressed the thought?
Not all stars are equally bright" or **Stars vary in brightness.