Some people consider them synonyms and others as separate species and that is why both appear. I will investigate the current consensus opinion.
If they are considered synonyms then Russual sanguinaria is the correct name and Russula sanguinea and Russula rosacea presumably treated as later synonyms -but needs checking.

I am sure you all are aware that Russulas in N. A. need work, but I'm adding this bit to this tag since I don't want this to get merged, just point out that there is a lot of work to be done on Russula and I am pretty certain that this is not going to be in the east N. A. despite all of the 600+ observations of it there. Mycoquebec has this as a synonym of Russula sanguinaria as well, mentions it is with conifers and it is probably a cluster of at least two closely related species. Steven Russell doesn't have it or sanguinaria for Indiana (not much pine). If people can help take those out of this species may be the AI will stop suggesting it.

Looking at this again in the literature I see a couple of articles (Singer) on the confusion of names here - lepida, rosea, rosacea, ruber etc . I think some authors consider R. rosacea to be a nomen ambiguum and it's use really a misapplication rather than strict synonym, hence the non-applicability of priority. Equally problematic is the co-existence of R. sanguinea and R. sanguinaria. The former being illegitimate and the latter a replacement name , as far as I can tell from a brief survey anyway. If correct then a future swap would need to knock all non European. Russula rosacea/sanguinea/sanguinaria back to Russula, and European records to R. sanguinaria. But somebody needs to look more closely at the taxonomy and nomenclature.