A timeout is silence. Your browser sent the request and waited, and nothing came back, not a page, not a refusal, nothing. Either the server is too overloaded or down to answer, or something on the path (a firewall is the usual suspect) is silently discarding the packets instead of rejecting them.
ipconfig /flushdns; on macOS run sudo dscacheutil -flushcache.example.com:8080 while the site works on the normal address almost always means the wrong port or a firewall rule covering that port.Visitors timing out while the site works from inside your network means the outside path is broken: check that the service is listening on the public interface (not only localhost), that the cloud or host firewall allows the port, and that the machine is not out of CPU or memory. A firewall that drops rather than rejects produces timeouts, which is why your own tests from an allowed address can pass while the public internet sees silence.
One site timing out everywhere for a day or more means the service is down, moved, or gone. Every site timing out on one network only means the router, modem, or provider path is broken; the phone test separates the two cases cleanly.
How long does Chrome wait before ERR_CONNECTION_TIMED_OUT? Chrome waits for its built-in connection timeout, which is long enough to feel like a hang, then gives up. There is no user setting for it, and the wait itself is the symptom: a healthy server answers in well under a second.
What is the difference between timed out and refused? A refusal is an immediate answer from the other end saying no. A timeout is no answer at all, which usually means a firewall is silently dropping the traffic or the server cannot respond. The fixes differ, so the distinction matters.