The only journals that have impact factors are those indexed by Clarivate's Web of Science, as they calculate and release the annual Journal Citation Report (as J.P. mentioned already) containing that metric. Thus, only the official impact factors contained in that report are "authentic". But as you have found, there are a handful of other citation metrics including Scimago Journal Ranking, CiteScore, Source-normalized Impact per Paper (SNIP), and others. Each of these metrics is slightly different and not directly comparable to each other or to impact factor. You can certainly use them and some may actually be better than IF, but they are not the same thing. Importantly, they are not inauthentic or incorrect, just different.
It's worth noting that sometimes sketchy journals will advertise these metrics in place of a an IF, watch out for that. Having (or not having) an impact factor doesn't mean a journal is good or bad, but lying about it (or trying to pass off another metric as an IF) is suspicious. On top of that, sometimes aggregate websites are not particularly careful about reporting IF and will scrape any citation metric and add it in that place.
Unless you have Clarivate's JCR, you have to rely on journal-reported impact factors. And any free website aggregating these (unless they have access to the original report) are probably scrapping the IFs from the internet. So again, they are not necessarily inauthentic. They may be outdated, misreported, or in the case of predatory journals, made up though. So really all of those websites are reasonable ways to try to quickly compare impact factors (or other metrics) but be aware that you'll need to verify the info that they provide. As far as I know the only way to have the complete list of impact factors would be to purchase the JCR at the source.