I have seen the question posted on this forum so many times! It is a common inconsistency with any backlink reporting for all the reasons stated above. The important thing is for you (or your clients) to not get caught up on the actual backlink numbers. Backlinks are just a fraction of all the different aspects of SEO. It is fine to use as supplemental information, but that is just about all you can do with it, since it is so inconsistent.

Instead of focusing on how many backlinks are out there (because once out there they are out of your control, and so is the data), you might change your reporting to list how many backlinks you have added/pursued in your SEO efforts for your clients. That way you are accountable to your clients for the things you have some control over, and not trying to explain numbers to them over which you have no control.