> I am not sure that partnership or ownership really changes anything.

It changes everything. DDG is a Yahoo customer and, as adrusi wrote, sources search data from them among other providers. Yahoo doesn't control DDG, its privacy measures, data collection, or product direction as they would as a parent company. The relationship is completely different.

I do agree with you about Searx having the optional self-hosting advantage. DDG claim they won't track you, but there's really no way to be certain.