Following advice I received through the community for a different issue, I applied the Visits metric to the entry page dimension and then did a referrer breakdown. I would like to understand why visits using the Entry Page dimension are little more than half the visits using the Page dimension.
To make sure we are on the same page (ha!), are you seeing something like this fake data?
If so, then the reason for the two different values is this ::
Report 1 shows how many times the home page was the very first page of the visit (aka the entry page). In this fake report, the home page was the very first page of the visit for 501,524 visits.
Report 2 shows how many times the home page was seen at any time during the visit. It could have been the first page of the visit. It could have been the 5th page in the visit. It could have been the 10th page of the visit. No matter at what point the home page was viewed during the visit, it will show up in this report.
Another way to look at this data would be adding the "Entries" metric to the Page Report. Doing that, you would see a report like this: