Native US English speaker here, and this is the first time I have ever heard of this. TIL
For that matter, the missing word could be this, as in “Friday (this) week” versus “Friday (that (as in the next one after the one contrasted with via the word this) week”. I have no way to disambiguate this, so I ask something like “Friday after tomorrow” or “Friday the 13th” or something. It’s hard being me at times, I’ll admit.
Next Friday is sometimes too ambiguous, you can never be sure you share the same definition with the other person. Is it the same as This Friday (the very next occurring Friday), or Friday Week (ie next week's Friday).
Maybe I should ask my kids...
Interestingly they both had different definitions of Next Friday though, and both thought there was only one way of defining it.