I too saw behaviour like this (the button's gone again now) -- what's interesting here is that with the examples you give, and the stuff I tried, it is almost as if 'searching harder' brings more 'word variations' into play. (It's a shame that the button has gone now, I didn't get a chance to play with it properly -- I might even recall some kind of 'search within these results' functionality being there too)
Also, as if almost to back up this idea, it seems that the recent google ranking changes having devalued word variations vs. the exact word. i.e. I had some pages that were ranking well on searches for widget安idgets安idgeting (/etc) because of google's word-fuzziness (synonyms), and now, the pages that have crept past me over the last month (or so) to rank higher for some specific searches /seem/ to be beating me because they have more instances of a/the specific keyword.
This is why you can search deeper for 'cars' (it has plenty of synonyms/variations) but not for 'Fred' (it has few or no synonyms/variations).
Hmmm.. I don't know if I'm explaining myself very clearly -- to summarise..
Before, it seems some of our pages ranked well when searching for widget安idgets安idgeting, because we used lots of these variations in our text.
Now, it seems that some of these pages are being beaten by pages simply using more repetition of the exact keyword -- e.g. search for widget, our pages using widgets安idgeting安idgetery are now not ranking as well as they were, these words don't seem to score as high as the exact matching word.
Competitors using the word 'widget' more times than us now simply seem to be ranking better than us (yes, of course this isn't all that is involved in the ranking -- I may be overlooking lots of complex stuff).
I think google are still making changes regarding the synonym/stemming/word-variation functionality they introduced a while back (it's almost like they're still trying to re-balance their results) -- and whilst what I'm observing in my results might be considered somewhat off-topic for this thread, my guess (in the absence of presently being able to study/research the new button any further) is that this new feature may be using a broader match on synonyms/variations. Or at least: it may have been introduced in an attempt to enable the average searcher to better leverage google's synonym-power.
It's a tricky feature to just throw into the mix (word variations, that is) and it would make sense if google didn't always weight synonyms the same for every search (let's face it, it can have the effect of making a search less exact), but perhaps gave them different weights / broader matching under some kind of user control. I think it's likely that this new 'search deeper' button is an attempt to put some extra google-power into the users hands by allowing a different set of parameters to be used (behind the scenes) for the searching (albeit, a pre-defined set of params), whilst allowing google to tune how that feature is being used in the main search (effectively backing it off).
It allows them to take a little of something away from one place and add it in in a larger quantity somewhere else.
End result, two 'modes' of searching: tighter more defined searches on a general basis, but with the ability to go deeper (by broadening the terms, and possibly searching within the existing data set (-- can anyone confirm this part? ...or was I hallucinating?)).
Just my 2p's worth -- these changes in the results are something I've noticed over the last few weeks, and as I did, I thought I should mention it here on WW at somepoint but hadn't got around to it until now.
Sorry if this seems a little of topic (..getting into changes-in-results and all that drudgery) -- but this all seems connected to me!