Probably like this
SELECT
artist,
title,
url,
FirstExtracted,
DATE_FORMAT(`FirstExtracted`,'%m-%d') AS Seconddate,
(SELECT COUNT(FirstExtracted) FROM results WHERE DATE_FORMAT(`FirstExtracted`,'%Y-%m-%d') = DATE_FORMAT(`LastExtracted`,'%Y-%m-%d')) AS FirstCount,
(SELECT COUNT(LastExtracted) FROM results WHERE DATE_FORMAT(`FirstExtracted`,'%Y-%m-%d') = DATE_FORMAT(`LastExtracted`,'%Y-%m-%d')) AS LastCount
FROM results
WHERE DATE_FORMAT(`FirstExtracted`,'%Y-%m-%d') = DATE_FORMAT(`LastExtracted`,'%Y-%m-%d')
GROUP BY Seconddate
ORDER BY DATE_FORMAT(`FirstExtracted`,'%Y-%m-%d') DESC
LIMIT 20
But why do you do a count in combination with a limit...?