Google Analytics is a tool that can be used by website publishers to better understand how people are using their website.
The Google +1 button is a social sharing tool that website owners install on their pages to make it easier for people to share their content on the Google+ social network.
The Google Analytics cookie stores a unique identifier, so the website can recognise you if you visit again. It also tracks the browsing history; the IP address and its actual location, and what site the browser was looking at before arriving at the site.
By default, this information is shown to website publishers through the Google Analytics tools and is not shared with anyone else. Website owners can also add their anonymized analytics data to a Google-owned pool of information on sites in similar industries.
If a browser visits a website that is using Google’s +1 button, a cookie is set, whether or not the Google+ button is clicked. Its conventional use is to remember preferences associated with Google services, such as your language and what level of Safe Search you might be using.
Google say this cookie is also now being used to record when and where the +1 button is loaded in order “to maintain and debug its systems” and expires after about two weeks.
If you click a +1 button this would be linked back to your Google+ ID. In this case Google+ will take the ID of your Google profile, obtained from the cookie that stores your Google account ID, the URL, and other browser-related information.
However, websites may share anonymised analytics data with Google and other companies. Google has assured that no data from Google+ is sold or given to third parties.