Even though you received an answer from a native speaker, I think that, literally translating, 話せます should mean "able to speak", while the meaning of 話すことができます should be "can speak".

I'm not very sure what is the difference between "can" and "able", which Nelly-san explained above. But anyway, I think 話せます and 話すことができます have the same meaning. As you know, there are two ways to describe an ability and a possibility using a verb conjugation and a verb + することができる／できます. They have the same meanings, but ~することができる is often used in a formal situation ((ex.)explaining things) or written language whereas a verb conjugation form is colloquial. （at an office, you're an instructor) ここをクリックしてください。 このファイルを　〇開くことができます／△開けます。 (between friends) 今日は、映画に〇行ける／？行くことができる　？ うん、大丈夫、〇行けるよ／？行くことができるよ。 I hope this helps you a little.

The same