Who has the final say on the page.
Surfaces are the pages about you where you have it: your site, your profiles, your listings. You register them and align each one with the current version of your canon, each alignment dated against that version. The engines read them all, and they should read one story.
Corroborations are the pages about you where someone else has it. You cannot rewrite them, so they are recorded in a registry as dated proof, with a channel to ask for an update when your story moves on. Watching re-reads a page at the cadence you set, daily, weekly or monthly, and tells you whether it still answers, whether your link is still there, and whether the passage about you changed.
They are steps 3 and 4 of the method, and the conversion runs both ways: a page that changes hands moves from one registry to the other. See Surfaces and Corroborations.