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The answer to this question explains how できる can have more uses than just as a potential verb. However, are there any differences in usage between できます and します? They both seem like they can be used to describe something being completed.
e.g. 宿題ができました! vs 宿題をしました！
There is not much of a real difference between the two when kids say those in real life.
The main difference, however minor it may be, is that the topic (and focus) is 「宿題」 in 「宿題ができました。」 whereas it is the speaker him/herself in 「宿題をしました。」.
A more interesting difference is that 「宿題ができました。」 has another completely different meaning, which is "I have finished preparing the homework." said by the teacher. 「宿題をしました。」 does not have this meaning.
宿題ができました。
You would say this to mean 'I just finished/completed my homework'. Your homework is complete now.
宿題をしました。
This means 'I did my homework'. Your homework may or may not be complete. For example, if you say しました。 as a reply to 宿題はしましたか？ , you normally mean you have completed it. But you could also say 宿題をしました。まだ最後までできていませんが。(I did my homework. Though it's not complete yet.) as a reply to 'What did you do in the afternoon?'
