The results differ between the Gmail api and Gmail web ui when using the standard query format as described here - https://support.google.com/mail/answer/7190.
The i
You can list the messages with second accuracy if you would like:
q = after:<start_of_day_in_seconds> AND before:<end_of_day_in_seconds>
So e.g. from Wed, 25 Nov 2015 00:00:00 GMT to Wed, 25 Nov 2015 23:59:59 GMT would be:
Wed, 25 Nov 2015 00:00:00 GMT
Wed, 25 Nov 2015 23:59:59 GMT
q = after:1448409600 AND before:1448495999