Can/be able to

Can someone please teach me the difference between the two?
I differ them by following my instincts therefore I can not explain!
Thank you in advance.

I would say the mean exactly the same thing.

First the=they

I’d agree with rjtrudel. I use them interchangeably.

their usage is not actually interchangeable in some contexts and tenses… especially the past tense

could you write some sentences which you are not sure about?

  1. He could write a letter to her. ( We don’t know if he really wrote a letter or not? )
  2. He was able to write a letter to her. ( I suppose he did write a letter. )

Am I right?

I agree with dooo.
For example, it’s not correct to say “I will can…”. The correct form should be “I will be able to…”. There are other examples in the past tense.

A correct example:
“I can’t speak well, but I will be able to speak much better in the future.”

Hope it helps.