@matigo Your question is probably a lot deeper than I understand. Basically, you store the data you want to store. You present the data you want to present. So, for example, I have links to posts of yours at matigo.ca. If you had a micropub server, on your site or elsewhere, as I have, it would receive webmentions from me. You could choose to store all or none of the payload, and display whichever bits of it you want to.
I'm storing my data. You're storing your data. Webmention is tying us together, if we want to be tied together.
And microformats are telling our various systems which bits mean what.