What does it mean when Uplink's public access server turns orange? I connected to it, and couldn't find any difference.

All it means is that you have it highlighted from your server listing.

On the main server listing you get when you aren't connected to anything, there's a button to both the left and right of the server names. The one on the left deletes the server from your listing, the one on the right toggles it's status on the world map. No button means it won't show up at all, the default shows it as white, and the second status (+) turns it orange. All it really does is make it easier to see that server on your worldmap when you're trying to fish through umpteen million servers and/or connections.

If you have an active mission at a server, it'll show as green instead of white or orange. I'm pretty sure that's regardless of the toggle (although hidden still hides it until you reveal it again).