I'd say, today being Monday, May 5, that this Wednesday is May 7 and next Wednesday is probably May 14. I might also refer to May 7 as "this coming Wednesday." If today were Thursday, May 8, I'd probably say that next Wednesday was May 14, but if talking about May 7, I'd probably say "this past Wednesday" if there weren't something else that unequivocally identified the day as May 7. Maybe on Saturday, May 3 or even Sunday, May 4 I might say that next Wednesday and this Wednesday were the same date, i.e., May 7. These distinctions are mine and I would not necessarily expect other USns to have the same criteria. If I thought there was any possibility of confusion in the mind of my audience I'd specify the date. If some other USn spoke of next Wednesday or this Wednesday I'd confirm the date.

Is that confusing enough?