Could or was/were able to

Hi there teachers,

Somebody told me that the difference between the past form of 'can' - could and the past form of 'be able to' - was/were able to is that "could" is used to talk about a general ability in the past and 'be able to' is used to talk about both general and one-time ability in the past. By the way, is that true, teachers?

He also gave me a few examples to show the difference:

1). He could run for 10 miles at a stretch when he was young. 
        Or 
He was able to run for 10 miles at a stretch when he was
young.

2-). When the boat was about to sink, he was able to/he managed to jump off it. 
(Not: he could jump off it.)

3). His wife was very angry with him, but eventually, he was able to/he managed to make her calm.  (Not: he could make her calm.)

Dear teachers, I don't know if what that guy told me about this difference between 'could' and 'be able to' is right. I just want your opinions on this. Is there really any such a difference between 'could' and 'be able to'?

Thank you.