No but we can and should store it as a timestamp with a timezone. It is rare for a nominal (date)time to be the correct thing to use. Please do read my other comment.
It would be highly unusual and misleading to call something a timestamp unless it is a point in time. In Postgres for instance, the timestamp with timezone type represents an instant in time.
This data type cannot be used to store things like reminders for future appointments. It's not rare at all.
Something that often trips people up is that they think timestamptz stores a timestamp plus a time zone (probably because of its unfortunate name). It does not; it always stores a Unix epoch without an extra time zone, converting any zoned timestamp that it is passed.