You could explain away the discrepancy by saying that the 45 billion number is the number of permanent residents. As the seat of a galactic empire it would like

You could explain away the discrepancy by saying that the 45 billion number is the number of permanent residents. As the seat of a galactic empire it would likely host representatives and their staff and families from tens of thousands of worlds, would probably be a hub of interstellar trade with many merchants and the crew of their ships staying for weeks at a time, a major tourist and religious hub with billions of visitors and pilgrims, countless numbers of galactic citizens would also make the journey to petition the emperor for various things. The list could go on for a mile and could result in a much larger effective population at any one time.