The difference between paid and organic search results.
Paid search results
Paid search results are essentially ads. With these, your search result placement is usually based on the amount you're willing to bid, and other factors like the quality and impact of the ad. You can do this through Google, Bing, Yahoo, or any other search provider with whom you can set up ads. Paid search results usually show up first with an “Ad” indicator.
Note that if your site violates Google's Terms of Service, you'll get removed from search results entirely.
Organic search results
Organic search results are unpaid results that show up organically.
When someone Googles something, Google's looking at that search query and determining which pages on the internet are reputable and relevant to your search. It then displays those results ranking them based on that relevance. The top results get clicked most often.