I still find it awkward and counterintuitive for most people as a pre-clickthrough button though.
You can also manage sites manually from the settings. flower in the top right -> search settings -> block unwanted sites
Sharing on Google+ creates a more prominent but soft broadcast/recommendation/endorsement to the public or to your friends (via circles).
Out of curiosity, I tried two scenarios:
+1 button on a website/link = I shared with a circle and it counted as a +1 automatically. This is NOT what Google is doing when you share a search result, so you are not +1'ing that shared-from-the-search-results url.
Sharing a link directly through the Google+ UI at plus.google.com = NOT automatically +1'd. This is what Google is doing with the 'share' link in search results. Sharing a search result does not +1 it while it does broadcast it to the circles you choose.