Do yesterday and one day ago refer to the same time period? If no, what is the difference?
There is no real difference that would be recognized and respected by all writers and readers.
However, I can see some justification in separating the two. If it is 6 o’clock in the morning, then yesterday could refer to any time before you went to bed for the night during the previous day, including for example 6 at night.
On the other hand, a day ago would be more apt to refer to a time close to exactly 24 hours earlier, so 6 in the morning again.