the site we're so merrily avoiding mention of is likely the Wordwizard Clubhouse.

the shortened hyperlink (link) is also sometimes referred to as an abbreviated link. we're sorry that there's no one word to use for it other than link; but there's usually no need to distinguish between a link and a shortened link, except when you get someone posting "long links" which can disrupt a forum. and then you merely need to call attention to the forum's posting toolset, which in our case has a button labeled "Create a link to a webpage" -- note the choice of wording here.

if we were to get into the underlying code or markup of links, this would probably make more (or less) sense, but.

in summary then, a hyperlink is a link is a hotlink is a weblink. YMMV.