I think it's a translation thing or translators don't know the difference
It's likely a translation thing, specifically a mtl issue. I don't know korean so I'm not sure, but just as an example from my own native language, I know that stepbrother is "velipuoli" (brother-half) and a half brother is "puoliveli" (half-brother). At least I'm pretty sure those are the words, the last time I had a close friend where we talked used terms like this was over a decade ago.
Either way, seeing how similar the words are, I wouldn't be surprised if Korean has something similar that stumps MTLs. Don't know for sure though.
It’s very clear their half siblings, given they have the same dad lol, it’s probably in the translation error. I like how devoted her brother is to her, is so cute such a protective brother, and the duke and his son are so protective as well! I also think the red hair woman was played or maybe she was plot against, but it was as if she was a traitor but wasn’t, maybe that’s why her son got away in the previous life