Is there a difference between a 10060 error and a 10061 error?

Yes, while both indicate connection problems, they have distinct meanings. 10060 typically means 'Connection Refused' or 'No route to host' – the connection attempt was refused or couldn't find a path to the server. 10061 specifically means 'Network unreachable,' indicating that there's no route to the destination network. 10061 is often related to routing table issues.