How the difference is counted
The gap between two dates is shown in two ways. The calendar breakdown counts whole years and months first and then the days that remain, which is how people state ages and anniversaries. The totals count plain days, full weeks, working days from Monday to Friday, hours and minutes. By default the end date itself is not counted, so 1 January to 2 January is 1 day. Turn on the end date toggle to count it as well, which is common for bookings and billing.
Months of different lengths
Adding months keeps the day of the month where it can. When the target month is shorter, the date is clamped to that month's last day, so 31 January plus one month lands on 28 February, or on 29 February in a leap year. The tool points it out whenever this happens. The same rule decides that a 29 February birthday is celebrated on 28 February in non-leap years.
ISO week numbers
Week numbers follow ISO 8601, where week 1 is the week that contains the year's first Thursday and weeks start on Monday. That is why the first days of January can still belong to the last week of the previous year, and 29 to 31 December can already sit in week 1 of the next one. To turn a date into a Unix timestamp instead, use the Unix Timestamp Converter.