We address this problem by saying that "past/last/previous" (units) are always at the last complete entry (and these terms are all synonymous), while the "current" (unit) is the incomplete entry in which we find ourselves. This consistency takes a small bit of practice, but eliminates ambiguity.
Right now let's pretend it's 12:32:40 PST.
- The "current hour" is the one that began 32 minutes ago (incomplete).
- The "past hour" ran from 11:00:00 - 11:59:59 (complete).
- The "current minute" is the one that began 40 seconds ago (incomplete).
- The "past 60 minutes" ran from 11:32:00 - 12:31:59 (complete).
So you see that when you need greater fidelity, you increase the resolution of the units.
Weeks always start on the same day, and days always start on the same hour, but whether this is Monday 00:00:00 UTC or Sunday 00:00:00 PST would depend on the organization.