Redirect
An HTTP response that tells the browser to go somewhere else, using a 3xx status and a Location header.
A short link is a redirect and nothing more: the server looks up where the key points, answers with a status and a Location, and the browser follows it. Everything a shortener knows, it learns in that one request.
The status matters. 301 says the move is permanent and browsers may cache it, which means a repeat visitor might never ask again and the click never gets counted. 302 and 307 say temporary, so the browser asks every time. A shortener that wants to count clicks and allow the destination to change uses a temporary status for exactly this reason.
Chains are legal and common: one redirect leading to another. Each hop costs a round trip, and each is a place the chain can break.