Sorry I read your post incorrectly. If I say, let's do something this week, it means up to and including Sunday. If I say next week, it means after the upcoming Sunday.
That makes sense for places where the week starts with Monday, but I guess this week means up to and including Saturday for Americans if it's actually normal that the week starts with Sunday.
I was always under the impression that Americans basically agreed on that the week started on Monday, that the weekend ended with Sunday and that next week meant after Sunday. I thought Sunday as the first day in American calendars was a "yeah, it's stupid we do it like that, but I guess that is how it used to be back in the days" kind of thing.
I disagree with the sibling poster. Your first paragraph is correct.
The week starts on Sunday. The weekend ends on Sunday. It only makes sense if you consider two adjoining endpoints of previous weeks to be one "weekend", which I've never known anyone not to do without thinking about it.
Someone talking at work might mean something different, but I don't usually hear "next week" to mean Monday-Sunday in general conversation and we'd probably clarify for Sunday anyway.
If someone says "The week of the 15th" and Sunday is the 15th, they mean the seven days from 15-21 not the seven days of 9-15.
"Next week, maybe Sunday" means the next calendar Sunday as in Sunday-Saturday, not the Sunday after that as in Monday-Sunday.
Anyone who says otherwise is selling calendars with a Monday start of the week. :)
Your 2nd paragraph is correct. No one actually thinks about when the week starts, it's almost universally understood to be Monday based even if the calendar says Sunday based.