Which error indicates a server is overloaded or has failed to respond?

The indication that a server is overloaded or has failed to respond is accurately reflected in a 502 error. This specific error, known as a "Bad Gateway," occurs when a server acting as a gateway or proxy receives an invalid response from an upstream server. Essentially, this means that the server did attempt to connect to another server to fulfill a request but encountered issues that typically stem from that upstream server being unable to respond appropriately.

In contrast, a 404 error signifies that the requested resource could not be found on the server. A 401 error relates to authentication, indicating that the request has not been applied because it lacks valid authentication credentials for the target resource. A 500 error indicates an internal server error where the server encountered an unexpected condition that prevented it from fulfilling the request but does not specifically denote an overloaded state or failure to respond as clearly as a 502 error does.

Thus, a 502 error is particularly relevant when assessing issues related to server responsiveness and load, as it directly connects to instances where intermediary services are unable to receive valid responses from upstream servers.