If you connect to a different server, the values will be different, but I bet you already knew that. Furthermore the documentation of the DataSource
property mentions that the state of the connection (open or closed) can affect its value. I don't know about the Server
property.
If you are looking for a way to identify "equal" connections, you may want to use the ConnectionString
property. This is how Connection Pooling determines whether a closed connection can be reused.