It was spelled both holy day and holiday (first recorded in 1460).
Originally, holiday referred exclusively to special religious days. However, the definition expanded to include secular days
The OED defines holiday as “a day on which ordinary occupations (of an individual or a community) are suspended; a day of exemption or cessation from work; a day of festivity, recreation, or amusement."
Thus, today, the word holiday is often associated with vacation.
The term holy day exclusively refers to a religious or sacred day.