Network System tray Icons

My Windows 7 system sometimes shows the System tray network icon (or the same with a red cross on it), and at other times it shows .

What do these icons mean?

In both cases, if I hover over the icon it says I've got an internet connection...

Thanks - Rowan

Thanks for your reply.

In that case, it's broken then, because I never have a wired connection. Sometimes it must be failing to recognise that it's connected wirelessly. Why would that be? Would it have any adverse consequences, or help to explain any of the odd things that now and again happen to me (blue screens, hangs, things going unbelieveably slowly etc.)?

What does the "wired connection" with a red cross on it mean? When this happens I still see "Internet Access" if I hover over the icon (and I normally do have internet connection).

Thanks - Rowan