The contract-based party numbering, first and third remain in common vocabulary, does not distinguish the browser or user as zeroth party. Putting tags on a page that cause tracking ads to run from unrelated businesses and their servers is the only useful “third party ad” definition here. Browser-based ads that use anonymity tech are a different category.

If you insist on a reductionistic definition that rules out anything other than a static ad on the same site as the publisher, you will get stuck trying to improve the Web and how it is funded. I understand objecting to all ads other than static images that click through into same origin forms, or whatever, but that won’t pay the bills for most publishers.