話せます and 話します
What is the difference?
Well, for starters, both are different inflections of the verb 話す, which means "To speak". The first one you typed, 話せます, is the potential form with polite ending, meaning " can speak". The second one, 話します, is exactly the same as 話す ("To speak"), only using the polite ending ~ます.
- I speak Japanese. = 私は日本語を話す (standard)
- I speak Japanese. = 私は日本語を話します (polite ending)
- I can speak Japanese. = 私は日本語を話せます (potential form, polite ending)
Also, the potential form without using the polite ending would be 話せる。
- I can speak Japanese. = 私は日本語を話せる (potential form, no polite ending)
Unless someone says otherwise, I think the use of を is a mistake here (or at least strange). The potential form in this case will take が:
"The potential form indicates that something is possible but no actual action is actually taken. While the potential form is still a verb, because it is describing the state of feasibility, in general, you don’t want to use the direct object 「を」 as you would with the non-potential form of the verb." - http://www.guidetojapanese.org/learn/grammar/potential
Outside of the specific lesson on verb stems and polite form conjugation (and a few example sentences here and there) Tae Kim almost exclusively uses casual/dictionary form when teaching. Much of finding a verb stem and conjugating is based on the dictionary form's ending and if you already know that form and know how to conjugate to a polite form it isn't really necessary to re-cover it every time.
The beginning of the "Essential Grammar" chapter in Tae Kim covers polite speech :)
I had found that page, too, but I'm still unable to extract the rules for creating the above form from the verb stem. The page about polite speech does not mention the potential form either.
I learned that 話し is the verb stem. I learned that 話せる is the casual potential form. I still did not find a rule how I get from there to 話せます (polite potential form).
But maybe I'm just too stupid.
話ます does not exist.
話す is the dictionary form of the verb and the ending す is the part that conjugates to し when in polite form.
You can only add ます directly after the kanji if the dictionary form of the verb ends in an "iru/eru" sound such as 寝る 'neru' sleep which becomes 寝ます nemasu
If the question was related to ability you were probably marked wrong for writing 話します because the sentence required the potential form of the verb 話せます・話せる
Either that or it was along the lines of "we will have a talk" where 話 was actually being used as a noun pronounced "hanashi" and combined with the verb する・します "to do". As a noun is the only time 話 uses "shi" is part of the actual reading.
話をします - to do talking, to have a talk