[rlhamil]

How about this: a date, or indeed even a time, is either of the shortest unit used in calculation at some moment (say by convention, the start of the date or time expressed perhaps down to nanoseconds); or it is a range, from the start of the date or time (expressed in terms of the shortest unit used in calculation, unless you want to fiddle with going down to Planck times to allow for future increase in precision) up to but not including the start of the next increment at the stated precision (for a time in seconds with a minimum resolution of nanoseconds, the billion nanoseconds starting at the beginning of the second).

So,an hour range starting at a half hour boundary might fall entirely within a day, entirely outside that day, or half in that day and half before or after it.

All of that neglects time zones, or assumes they're at most recorded for local convenience and/or historical purposes but converted for calculation into UTC or the like.

So, for instants, either they're equal or they're not; but for ranges, they could be equal, or a smaller range entirely within a larger, or partly overlapping, or disjoint. Pick whichever model (instant or range) works best, and be consistent thereafter, and at least the surprises shouldn't be too surprising.