Difference between "one..., another" and "one..., the other"

I have searched on the internet but the explanations are in Chinese, which I can't understand.

What is the difference between these two (pairs of) sentences?

  • I have 2 pens. One is red, another is black.
  • I have 2 pens. One is red, the other is black.

Solution 1:

It has to be:

'I have two pens, one is red, the other is black.' You cannot say 'another' because that suggests there is more than one. And if there were only two to begin with, there can only be one.

But if I started out with three pens, I could say:

'I have three pens, one is red, another is black'.