For time expressions with comparative adverbs like earlier, later, you have:
- earlier or later in the day, week, month, year, evening, etc.
He has breakfast at 10:00 am, not later in the morning. [conjures up a specific time, like at 11:00 or 11:30 even if a specific one is not given.].
later in the day: at any specific point when the day is still the day.
While: earlier or later during the day, week, month, year, evening, etc.
He has breakfast at 10:00 am, not later during the morning. [could be at anytime after 10:00 am that is still morning.]
later in the day: suggests there will be a specific time while it is still day.
later during the day: suggests it will not be at night or at dawn but does not suggest a specific time like "later in the day".
Please note: When I say it suggests a specific time, I do not mean a time has to be given precisely. Whereas during refers to an entire time period without suggesting a specific point in that time.