There's yet another proposal for embedded representation of a URL on 3rd party sites, see my previous post on Open Graph and JSON:LD.
oEmbed allows a website to display embedded content (e.g. photos or videos) when a user posts a link. Contrary to the other approaches, oEmbed requires implementation of a dedicated service endpoint (i.e. not simply some
meta HTML tags). It seems to be used by WordPress and Slack (at least the later also can do alternatives).
The act of obtaining embedded information seems to be called 'unfurling' (improving preview of an URL).