For DVC resort point charts, one week means 7 nights, where every night is within the same season (Dream, Magic, etc.).
For World Passport Collection resorts, one week means 7 nights, with the check-in date determined by whatever an owner at that timeshare resort has deposited. The most common check-in days at timeshare resorts are Friday, Saturday, and Sunday. But some timeshares allow Thursday and/or Monday check-ins, while some others have only Saturday (or only Friday and Saturday) check-ins.
Actually a week is 7 nights, not days. I know that's a fine distinction, but it's significant. If you check in on a Saturday, you check out on a Saturday. So you have use of the resort facilities for a full 8 days. (Of course, you have to be out of room by check-out time on the 8th day, but you can still use the facilities.)
For a DVC resort stay, it truly does not matter "which day of the week you start your vacation." Nor do you have to stay exactly 7 nights.
But for a World Passport Collection stay, it does matter. If a timeshare resort on the World Passport list only allows Friday and Saturday check-ins, you can't plan on a 7-night stay starting on a Thursday.