Other and another

I'm going to say that 'the other apple' is a specific apple. You ate one and this is the other.

If you have a bunch of apples. You ate one, and another is in the fridge. We don't know what happened to the rest of them.

I would use "other" in that sentence.

"Another" indicates it's in addition to what is already there.

I bought two apples, one was red, and the other was green.

I bought a red apple, then purchased another apple which was green.

Hi all,
I have appreciated all the clear explanations. Thank you very much.

Did you mean "another" is an equivalent of "the rest of the apples," Roger?

No. Another is only one, and could be any one of the rest of the apples.

I hope that helps more than it hurts.

Take the example of the OP:
I bought two apples, I ate one and the other/another apple is still in the fridge.

When there are only two apples, we have to use "the other" rather than "another;" while there are more than 3 apples, we have to use "another" when we don't specifically point out the particular one of them?

That is, in the OP case, he/she has to use "the other" but not "another?"