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.