能力って英語でなんて言うの？

First, let me say, great question!

Whilst the two words are often used interchangeably, there is a subtle difference between the two.

Ability refers to how much one can do in the current moment, how much one has developed a skill so far.
Whereas, capability refers to how much potential one has to develop a skill, what they could achieve if they continued to work at it.

When you are the best you can possibly be at something, your ability and capability will be the same.

Example sentences:
"The gold medalist proved their running ability was the best in the world right now. However, experts believe the silver medalist has the capability to win in the next event."

"The teacher was concerned about the student's writing and reading ability, though she continued to believe that he had the capability to improve."

The first phrase refers to the fact that the person is already equipped with the skills to achieve their goal, such as gaining a place at university.
The second phrase focuses more on the potential of the person to achieve their target, and infers that, provided they apply themselves to the task in hand, they are capable of achieving this.
The third phrase contrasts the slight difference in the two words. The first part of the sentence states the persons ability as a fact, and the second part refers more to their future potential.

We would use the word, "ability," to talk about a skill that someone has/hasn't to do or complete a task.
Example sentence : He has the abilities needed to be a great craftsman.
We would use the word, "capability," to talk about a conditional idea that someone has the ability to do something if they wanted to. This word caters more to the possibility or something and isn't certain yet.
Example : He has the capability to be a great craftsman if he tried harder.

The best time to use the word capable, is it to use it to describe personality or nature of a person or thing.
Being able to do something means that it can be done, it is possible.
They are interchangeable, but these are the safest ways to use these two synonyms.

The words "ability" and "capability" have similar meanings with very little difference. The key difference when you speak of someone's capabilities is that it implies the potential to be able to do something rather than just actual ability.
You may use these terms in a sentence in the following ways:
-The job requires the ability to travel when needed. It's important that the candidate should not have family ties or children.
-The candidate for the job should be capable of working in a team, meet deadlines and pay attention to detail.

I have the ability to approve this client's loan.
He has the capability of winning gold in next year's Olympic.

When you know someone can do something, you know their ABILITY.
She has the ability to win the entire competition!

When you know how someone can do something, you know their CAPABILITIES(capability).
She is the only one in the game that can actually play.