1) Using remote administrator to access one server.

2) Query Analyzer to reach local server and running the same query.

a) With IP, 20 seconds.

b) With Servername, 20 seconds.

c) With ".", 35 seconds.

Some time ago I remember why,  now I can't.

Beside Alzheimer jokes, anyone can help me?

There's something called a reverse DNS lookup if you supply an IP address instead of a resource name.

Using just the period, of course you're connecting to the default local instance, but I assume DNS comes into play for that as well. And usually local instances are not on a fixed IP address.