What is the difference between multinomial and categorical distribution?

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:-

Bernoulli:Binomial::Categorical:Multinomial

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)