To me, Paul's example is a datetime operation: you start with a datetime
(7am today), perform arithmetic on it by adding a period of time (one
day), and get a datetime as the result (7am tomorrow).

Well, OK, let's propose these wordings: It looks like a date
operation, ie, add one to the date, but in reality it's a time
operation, ie add 86400 seconds to the time. These things sound
similar but are very different.

I have to disagree.  If I have my alarm at 7am (localtime ;) so I can be at work at 8am I don't care exactly how many seconds have passed, that alarm better go off at 7am local time.