2nd day of the month
Refers specifically to the second day of a calendar month. Often used with month names or in date expressions.
会議は来月の二日です。
The meeting is on the 2nd of next month.
two days
Indicates a duration of two days. Often used with counters or in expressions like 二日間.
この仕事は二日かかります。
This work will take two days.
It took two days to finish this job.
Please take this medicine every other day.
May 2nd is a national holiday.
三日 (みっか) and 二日 (ふつか) are both irregular day-readings that beginners often mix up, since neither follows the regular Sino-Japanese number+日 pattern.
六日 (むいか) and 二日 (ふつか) are both irregular kun readings for calendar dates/day-counts that beginners often mix up or misread.