"No connection could be made because the target machine actively refused it." versus "The wait operation timed out."

These are two very different things. The second suggests an explict failure in interacting with SQL Server but the first doesn't really get that far. It suggests that there was nothing listening on the port specified or that the firewall is blocking you! These two different circumstances came up when experimenting with turning off a database needed by two different web services in two different environments to see how the web service would react in logging the error. It turns out it acted two different ways. The second was ideal. The first came up somehow by way of database mirroring and failover. You may do that sort of thing in a connection string like so:

Data Source=myServerAddress;Failover Partner=myMirrorServerAddress;Initial Catalog=myDataBase;Integrated Security=True;