¿Cuál es la diferencia entre "she didn’t get to finish a letter" y "she couldn’t finish a letter" ?Puedes dar oraciones como ejemplo.

Consider the difference between "I didn't get to say goodbye" and "I couldn't say goodbye."

The first one implies that you wanted to, but ran out of time. On the other hand, the second seems to imply a lack of ability, for whatever reason.

So, for example, if you have a homestay and you end up having to leave earlier than expected, you could write your host family saying "I'm sorry I didn't get to say goodbye."

On the other hand, if you were leaving and they saw you on your way out, but thinking about saying goodbye makes you emotional and you want to avoid those feelings, you could tell your friends later on: "I couldn't (bring myself to) say goodbye."

In your example, "she didn't get to finish the letter" implies she wanted to finish the letter, but due to circumstances, she ultimately did not get around to doing it. On the other hand, "she couldn't finish the letter" would make it seem like she has a disability that prevented her from doing so.

Maybe it won't be a perfect fit, but if my Japanese is correct, it would kind of be like the difference between 機会を逃した vs. 出来なかった