I am very sure about the use of contractions in positive and negative sentences. But I am not sure about their use in questions. I've seen many examples of the use of contractions in questions, but I want to know whether or not they are standard English. Consider, for example, the two following sentences:
What's he done today?
What has he done today?
How different are these two options? What register or style do they belong to?
In your example the sentences are both grammatical and mean exactly the same thing.
The choice of which to use in speech, can depend on where you want to place emphasis. If you are emphasising 'today', or 'done' it doesn't matter. But if you want to emphasise 'what' or 'has' it is better to use the long form. e.g.
WHAT has he done today?
What HAS he done today?
Contractions, whether in questions or otherwise, are more common in speech than in writing, and more common in informal than in formal situations. Having said that, uncontracted forms in speech (except in the most formal of situations) are becoming less common, and contracted forms in writing appear to be becoming more acceptable.
This Ngram shows one example of the increasing use of the contracted form.
