What meaning do the primary / secondary menu links have when it comes to SEO? Is there some meaningful difference between the primary / secondary links when it comes to SEO? Do they carry a different weight from a search engines perspective? 

Thank you!
Usually there is no meaning other than that you apply. For most sites, Primary links (or Main menu) are used to navigate the content of the site, and Secondary links are more for the infrastructure links (Contact, Site policy etc). You can use them any way you wish in the context of your own site. There should be no SEO impact.