The different feeling at night vs. the morning probably has to do with your body chemistry. Your blood sugar, blood pressure, hormone levels, etc. change at different times of the day and night. You're also affected by the amount of sunlight. Even with the shades drawn and your eyes closed, on a sunny morning you can probably still sense the sun's rays through your eyelids.

Also, if you are able to sleep in the morning, I guess it means you don't have to get to school or work early that day, which would make you more relaxed.