mainEntity, sameAs, url

Hi,

Whilst extending schema.org <http://schema.org/> for our BioSchemas <https://github.com/BioSchemas> project, I would like to try to do the “correct thing” with regard to interlinks between entities. I have found the documentation a little confusing/contradictory in its discussion of what these properties are for:
url
sameAs
mainEntity / mainEntityOfPage
about

In particular the descriptions of the properties give me a different impression compared to the discussion about them:
https://schema.org/Thing <https://schema.org/Thing>
https://schema.org/docs/datamodel.html#mainEntityBackground <https://schema.org/docs/datamodel.html#mainEntityBackground>

It would really help if there were some examples of usage I could be directed to. At the moment it is not clear to me how they are supposed to be used within a page, and pointing to pages (e.g. a website about an event) or abstract entities (e.g. an event itself). Any help gratefully received!

Cheers,
Andy