I am only interested in the meaning as relating to categories. I understand that there is only a "categorical denial".
For example would be there be a difference between
categorial storage of data
categorical storage of data
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However, it is always possible that in a particular field, a word might have a much more specific technical meaning. For example, as FumbleFingers said in the comments, in linguistics, there is something called categorial grammar, which is normally not referred to as categorical grammar. On the other hand, in logic, there is something called a categorial statement, which, however, is even more often called a categorical statement.
In your particular case, if you search google books for categorical storage and categorial storage, you will see, first of all, that the latter is much rarer. However, based on context, it seems (to me, at least) that it means the same thing as the former.
Having said all this, I would say that, to be sure, perhaps you should pose this question to the data science StackExchange.
categorial: of, dealing with, or involving a category
I think this is more common in US English, it's not common in British English.
categorical: without any doubt or possibility of being changed
Is not really applicable to data - its more about being emphatic in your opinion or statement... Its dealing with a different thing.