Categorical or Categorial? Is there a difference between the two terms from a statistician's point of view? I have heard about Categorical distribution and Categorical variables in statistics. But what is a Categorial variable? Can both Categorial and Categorical be used interchangeably? Are there specific cases in which we use either of these terms?

I have literally never heard 'categorial' (without the second C) and assumed that this was a typo. But some googling does indicate that this word is used - in linguistics.
In statistics, as far as I know, we only use categorical.
As mild support for this claim, if one googles 'categorial statistics', Google assumes you've made a typo and returns only results for 'categorical statistics'.
Also, searching for 'categorial' on wikipedia returns no links, but the closest suggestion is 'categorial grammar' (again, about language/syntax). In contrast, searching for 'categorical' returns a bunch of suggestions including several articles about statistics (specifically categorical data), maths and logic.
EDIT: This excellent comment by Scortchi may have tracked down the origin of the confusion to German and French distinctions that are mostly absent in English.
