I think the Firefox settings now call it the address bar when selecting if you want it to do both functions or have separate boxes. It may still be that internally.

Also I just looked it up and apparently I was wrong anyways and the Chrome internal docs call it the omnibox actually…

And the chromium developers blog calls it the address bar…

And so does The Keyword (blog.google)…

I think they’ve both given up on getting the public to use their special names now that it’s just an expected feature of a browser.