Both seem to result in one of k different separated outcomes, and Wikipedia says these are often conflated. Despite reading the explanation of the difference on the article about multinomial distribution, I still have trouble understanding what the difference really is.
The multinomial distribution is when there are multiple identical independent trials where each trial has $k$ possible outcomes.
The categorical distribution is when there is only one such trial.
Think of it like this proportion:-
So, just like Bernoulli distribution gives us the probability for a binary variable at each instance while Binomial returns it for N examples, Categorical distribution gives us the probability for a k-classifying variable at each instance while a Multinomial distribution returns it for N examples.
Thus: Categorical(Pk) = Multinomial(Pk, 1)