In the United States, President's Day, which commemorates the birthdays of George Washington and Abraham Lincoln, is a holiday, because federal employees and many private employees do not work on that day. However, it is not a holy day, because Washington and Lincoln are not gods.
In the United States Yom Kippur, the Feast of the Epiphany, and Eid al-Fitr are holy days--to Jews, Christians, and Muslims, respectively. We would say "Yom Kippur is a Jewish holiday, but it is not a federal holiday, a state holiday, or school holiday."