There are some parts of the SE interface which use vague timestamps, always rounded to a day:
On user profiles beside 'member for':
The actual membership time in this case (found in the hover text) is 14 minutes, but it all it says on the page is 'today', which is less useful (and not quite semantically correct: "member for today" suggests they won't be a member tomorrow).
In the sidebar on the right of questions beside 'asked' and 'active':
The 'active' time could be useful, but it isn't. I regularly check back for activity on questions I've interacted with, but I have to scroll all the way up and down to see if there is anything new, because the 'active' time just says 'today' regardless of whether it was updated 10 hours ago or 10 seconds ago.
The vague timestamps aren't saving space on the screen, so have no advantage. The use of 'today' also causes complaint about the time zone, which could be avoided in these cases by using 'X minutes ago'-style timestamps the same as everywhere else.