You’re right, of course, about the terminology that we commonly do and don’t use. The notions like “zeroth cousins” and “zeroth cousins once removed” are descriptive terms that describe how these relations stand with respect to one another, as in the “consanguinity” chart that @Dewey_Finn posted.
The entire second column in that chart are the “zeroth cousins”, and the entire row beginning with “Person” are the “zero times removed”.
The recent thread I mentioned, and the particular post (by @Chronos), is this:
Searching this Board for the phrase “zeroth cousin” finds about 15 prior mentions of the phrase.