Why is the ‘publications in common’ count different on my profile to that of my co-author?

The "Publications in common" count is based on the number of publications you and your co-author have manually confirmed as belonging to you.  

While you may have confirmed authorship of 4 publications, your co-author may have only had the opportunity to confirm 2.

This would be the cause for differing counts. Once both of you have claimed your publications in common, the counts will be identical.