See also: webmention, the plumbing used to notify posts that they’ve been linked to
A mention is not really a “type” of post from the publisher’s perspective (i.e. there is no “mention” UI), as any sort of post which can link can implicitly be a mention, as well as potentially being in response to another post.
Mentions typically don’t fit into comment/reply threads and therefore are often displayed separately, or in a more compact manner.
Unlike a like, a mention is not implicitly emotionally positive — a link is not always an endorsement.
IndieWeb examples displaying mentions to posts
Aaron displays mentions to posts on aaronparecki.com in an “other mentions” section below likes, reposts and comments, as well as giving the mention count in feed views (example).
Barnaby displays mentions to posts on waterpigs.co.uk inline chronologically with other responses, but in a more compact form that explicit comments, and displays mention counts in feed views (example).