It depends where you live. I use this coming and a week from. Next is simply not clear and interpreted differently by different people.
Today is Friday July 10. If I want to meet you Tuesday the 14th, the best is to use the date, but during a verbal conversation we rarely know the date off the top of our heads so I would say, “let’s meet this coming Tuesday.” I think that’s clear. If I wanted to meet up the 21st I’d say, “let’s meet a week from Tuesday.”
I can’t tell you how many times I am annoyed when someone says, “next Sunday,” and I try to clarify, “Do you mean a week from Sunday?” And they say, “yes, I said next Sunday.” Well, to me, if today is Friday, next Sunday is this coming Sunday in two days!
I don’t care if people define next differently, I care that they are so obtuse they get annoyed when someone tries to clarify, and actually seem impatient about it.