「今日は8月10日です。」 It's August 10th today. It isn't August 10th today. Is it Augsut 10th today? Yes, it is. No, it isn't. 「今日は何日ですか?」 What is the date today? It's August 10th today.
「昨日は8月9日でした。」 It was August 9th yesterday. It wasn't August 9th yesterday. Was it August 9th yesterday? Yes, it was. No, it wasn't. 「昨日は何日でしたか?」 What was the date yesterday? It was August 9th yesterday.