- CPM: you pay per impression (ie how often the ad is seen)
- CPC: cost per click. You only pay when the user clicks.
- CPA: you only pay when the user clicks and does something (eg buys something)
Display advertising (putting ads on third-party websites eg AdSense) is primarily CPM. Search advertising is primarily CPC (or at least this is how Google operates; I assume DDG is similar).
It's important to understand the implications of this.
In a CPC model the system that selects what ads to show you is doing so to maximize revenue. Since they only make revenue when you click a lot of effort is spent in determining the predicted CTR (click through rate) because:
Revenue = # of impressions x pCTR
So it's not just a question of who pays the most for an ad (that's how display advertising works largely) because a $1 CPC with 1% CTR earns more revenue than a $10 CPC with 0.01% CTR.
This is why I have less problem with the CPC search advertising model than pretty much any other model because your interests and the interests of the search engine are largely aligned. You want the results that are most relevant to you and that might be an organic search result or an ad. As long as the ads are clearly display as such, it's fine.
Also with search there is intent. You've searched for something so there's something you want. Who's to say an ad won't be the most relevant result?