@Fab
Firebug has been around a long time; it seems entirely likely that the built-in tools in many current browsers (certainly IE8's if you've ever looked at it) have been inspired by it, and it in turn has been inspired by unique features of browser's own inspectors.
Firebug itself enables further extensions. For example, if you are doing LAMP development, one of the nice things you can do with firebug is run firephp, which allows you to send debug information from the server side PHP to the browser via headers so that it doesn't interfere (generally) with the page operation. You can then view the debug output directly firebug's console. There are loads of nifty tools like this.
Note that firebug (lite) is also available for webkit browsers nowadays too
