Having worked directly with these communities and their material culture, this is what I was taught, but I am happy to be corrected if there is another better perspective.

EDIT: I checked, since I am old and sometimes out of date. The Smithsonian and Library of Congress have switched terms since about 2022 to Haudenosaunee. https://americanindian.si.edu/sites/1/files/pdf/education/haudenosauneeguide.pdf

Edit, Edit: I get the joke now, but you’re all trapped in here with me now, so here’s an info-dump: I used "Iroquois" interchangeably until about 2022, which is right around when the American Anthropological Association and the Smithsonian made the formal switch. While "Iroquoian" is still used as a technical linguistic category, "Iroquois" is being phased out as a name for the people because of its colonial origins and its potential interpretation as a slur. I remember hmming and hawing about it back then, but ultimately, as I’ve learned more about Indigenous sovereignty, "Iroquois" just feels increasingly dated now in any context.