The first time you logged into the server, it didn't have a key value associated with it's hostname in your ~/.ssh/known_hosts~/.ssh/known_hosts. When you accepted it'sits identity, you added the key. Subsequent log ins referenced that key value so it'sits identity was verified and you got no message.
When
When you logged in from a different system, one that had accessed this server previously, it has a key value that matched the current key on the host, so no message was displayed. To
To validate this. Log out of the remote hose, remove it's entry in your ~/.ssh/known_hosts~/.ssh/known_hosts file and then log back in. You'll see the "identity could not be verified "message"identity could not be verified" message again.