If you search any word or phrases, Google comes up with a lot information about that. The number of results is relevant to the topic. But in general, the number of googled key words are very high. Google has a very advanced mechanism, robots, that access to millions of websites. Also, google has another mechanism which is ultimate internet cache, cachedview.com. Therefore, you will be able to find some contents which have been removed, but still are reachable throw cachedview.com.
However, google doesn't have permission to all articles, theses and bibliographies. Dartmouth Library access to thousands of articles, journals, abstracts, papers and theses from Dartmouth College, the other Ivy leagues, the other top universities, even out of the United States.
So, to answer to the question, what is the difference between Google and Dartmouth Library, I would say Google is more public and is open to everybody. But, it doesn't give us all of the actual research papers and publications. You can find a lot of research papers throw Dartmouth Library which are not open publicly.