Let's imagine it's currently Wednesday the 1st. Does "next Saturday" mean Saturday the 4th (the next Saturday to occur) or Saturday the 11th (the Saturday of next week)?
No. This week is a rolling 7 days from the day you are on. "This $day" indicates the day that falls in "this week". You can use yesterday on sunday or "this past Saturday" to indicate the saturday that fell the previous 7 days.