Amazon is most like Facebook in that the ads are only displayed on its own property rather than all across the whole internet on any site that displays 3rd party ads. That, combined with the fact that Amazon also has a ton of data on its users just like Facebook makes them very alike (not that Google doesn't as well).
What separates Google from Amazon is that their paid ads can be displayed on any 3rd party site that they don't own, through DoubleClick. And of course the whole search engine monopoly makes that impenetrable for now.
Of course, it's all up for grabs, Amazon could go out and buy an ad network like Mediavine and go head-to-head with DoubleClick.