Surly the sites can differentiate between credit and debit, even I can tell that, the number formats are different.
But I agree whether or not the site stores the data I don't think credit or debit matters.
I believe (but do not know) that at least in the US, by law, they need your permission to store the card number. Of course, the law only matters to reputable sites.
I no longer see any worthwhile savings with Agoda and the like, I generally just book with the hotel.