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Not quite.
DuckDuckGo’s results are a compilation of “over 400” sources according to itself, including Bing, Yahoo! Search BOSS, Wolfram Alpha , Yandex, and its own web crawler (the DuckDuckBot); but none from Google. It also uses data from sites such as wikipedia, to populate knowledge panel boxes to the right of the search results.
X does it more like the second one, but there’s nothing stopping mastodon from doing it like the first.