Google is not against advertising. It is great for educating people, and alerting them. It can drive traffic to a site, and raise awareness. And there can be a lot many reasons for advertising, but Google has nothing against them.
But the simple answer to the question is, one type on link manipulates search engines, whereas the other type does not (you can guess which does which). When you're paying for links that pass PageRank, fundamentally, you are paying for something that manipulates search engines, something that creates the worst search experience for users, and hence violate Google's Terms of Service.
So you can use AdSense, DoubleClick, Chitika, or whatever you're interested in. What Google looks for is, whether search engines get worse, or whether PageRank is being passed, and whether search engines get manipulated by a particular set of links.
So if you have a link to your site that passed PageRank, then that will definitely harm your website more than it will do good. If you're doing advertisements just make sure those links don't pass PageRank and manipulate search engines in any way. Avoid spamming :)
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