I keep seeing both names come up in discussions about IQ testing but I am not sure they are even the same category of thing. Mensa seems to be a membership organization and RIOT IQ seems to be an assessment tool. Can someone explain what each one actually is, what they are designed to do, and whether taking RIOT IQ could qualify you for Mensa or if they serve completely different purposes?
They are different things serving different purposes. Mensa is a high IQ society that accepts members scoring in the top 2 percent on an approved intelligence test, roughly 130 and above. It is a social organization, not a testing body. RIOT IQ is a cognitive assessment built on the CHC model covering 15 subtests across 6 ability domains, designed to give you a detailed cognitive profile rather than a single threshold score. Mensa does not currently accept RIOT IQ scores for membership qualification, but what RIOT IQ gives you that a Mensa qualifying test does not is a full breakdown of your cognitive architecture rather than just a pass or fail cutoff.
Mensa tells you if you cleared a bar 
RIOT IQ tells you what your cognitive architecture actually looks like underneath the score. Those are useful for completely different things and honestly the profile is more actionable than a membership card.