Nice list of datatypes! Surprised I hadn’t seen this page before, having looked at type theory and such. These are all very familiar to me although I hadn’t seen them described in this way before. Handy! [it’s poorly linked to which is why i never found it]
So: both binary and categorical have incomparable relative differences. But binary is Bernoulli and categorical is categorical. Both can be analyzed by mode or Chi-squared. I understand mode: and it explains why I prefer frequentist over Bayesian on principle even though Bayesian in practice is very useful.
multinomial – many names. The arbitrariness of categories. It’s all in categorical data type. It’s also in binary but binary is 2 and what if you need more than 2 categories?