What us the difference Between “Destination Host Unreachable” and “Request Timed Out”?

If a request times out, it means that your computer did not receive a response at all.

The Destination Host Unreachable message means that a router sent you back an error and is equivalent to a busy signal.

Destination Host Unreachble is reported  when there is no routing to the subnet is avaible

for  example if defaut gateway is not defined  and the address you are pinging it outside your network then you get this message, or there no no routing availble onward path to the  destination

Request time out will be issued there is a valid path to the destination, however the ping response is not received due to a error or delay congestion on the path to the destination