Golly gee, Mr Malusa, I ve been doing this for 16 years now, maybe I'll learn this darn stuff someday.
Well, I've been doing it for 25. Typing in an incomplete URL and going NOT to a search results page but to the actual URL, sounds like your typing it in the Address bar. The behavior is identical.
The Firefox toolbar behaves as if you search from the main Google page. The Google toolbar must get search results from somewhere else or they are cached differently.