I've got two cars. One is black, the other (meaning "the second of two") is red. - Yes
I've got two cars. One is black, another (additional one) is red. - No. If there are only two in total, and you've talked about one already, then the second (of the two) should use "the other."
I have many cars. One is black and another is red. (This is an additional one, and there are still others not yet mentioned.)
If you say "the others" then you are talking about all of the remaining things.
I have many cars. Two are black and the others are red. (All of the remaining cars.)
Does that help at all?