Brave has bought a search company that became what is now "Brave Search". They are using their own index.
The "third-parties" bit, IIUIC, is the part when their index does not give good results and it falls back to working like startpage: they send the anonymized query to Google/Bing and take the results to send to the user. I believe that the idea is that they can use this as a way to improve their own index.
They also show on the results page how much of the results are coming from them vs from third-parties [0]
This is true for their normal search, but for their image search they always seem to say "results from third parties" if you click the info button.
Maybe their image search just hasn't encountered enough websites featuring the word "bird" or maybe their disclaimer is shown more often than intended, but I get the idea that image search is always done externally.
The "third-parties" bit, IIUIC, is the part when their index does not give good results and it falls back to working like startpage: they send the anonymized query to Google/Bing and take the results to send to the user. I believe that the idea is that they can use this as a way to improve their own index.
They also show on the results page how much of the results are coming from them vs from third-parties [0]
[0]: https://search.brave.com/help/independence