Without your error message it's difficult to be precise, but it is likely that the problem is that ToShortDateString is culture sensitive, and the information it returns will depend on how the computer you are running on is configured. Since SQL prefers it's date in yyyy-MM-dd format, try using ToString instead:
string str = "Select sponcorid,leftcount,rightcount,totcount,pair,createddate from Payout_Master Where createddate Between '" + Calendar1.SelectedDate.ToString("yyyy-MM-dd") + "' And '" + Calendar1.SelectedDate.ToString("yyyy-MM-dd") + "'";
However, I doubt if your query will return may records, given that both dates are the same! Did you mean to use two Calender objects?