In general, if I say:
From December 15th to December 16th
Would you expect the range to be from
12/15 00:00 to
12/16 23:59 or would you expect it to be from
12/15 00:00 to
The word "to" there could be interpreted to mean "until", or it could mean "through", so either of your possible interpretations could be correct.
On face value, though, with no other context, I'd assume your first option; that is:
would mean up through the 16th until 11:59:59.
IT would go to 23:59, because there are 59 minutes in an hour. My university assignments are due by 23.59 on the day they're due, meaning if it was submitted after midnight, it would be considered late.
With no further context, I'd assume it meant some time point on the 15th until some point on the 16th, quite possibly non-contiguous. It might even be into the early morning of the 17th, as night-time events that cross midnight are often labelled from the date prior to that midnight.
There would for example be a great many cases where "From December 15th to December 16th" would mean --12-15T09:00 to --12-15T18:00 followed by --12-16T09:00 to --12-16T18:00 or something similar to this, because those are common opening hours for businesses around here and therefore if they were doing something on the range of dates in the question, they'd be doing it on those hours. For much the same reason, it could be --12-15T18:00 to --12-16T02:00 followed by --12-16T18:00 to --12-17T02:00 if it is something people would be doing after business hours, and we might include the wee hours of the morning as part of the night of the previous days.
Not that I'd jump to the conclusion of any particular set of times like that, just that if there was no reason from context to assume a contiguous range, I'd certainly assume that it was a possibility.
Even with contexts like websites or other cases that are inherently 24-hours, I wouldn't assume it was from --12-15T00:00 to --12-16T24:00, because these things often aren't.