Holiday in the US can have a couple of meanings.
In general, "the holidays" is the time between Thanksgiving at the end of November to New Year's Day.
"Have a happy holiday!" or "Happy Holidays!" are generic greetings/sayings when you don't know what religious holiday someone celebrates, Christmas or Hanukkah or the Winter Solstice or nothing at all. Most people in the US celebrate Thanksgiving and New Years, so it tends to fit a variety of people without offending.
"Tomorrow is a holiday," usually refers to a day off from work, one of the scheduled Federal holidays, such as Christmas or Labor Day or the Fourth of July.
However, having several days off work, when you might go somewhere else, is a "vacation." Most jobs allow employees two weeks of vacation a year, sometimes more the longer you work there. When school lets out for the summer, it's "summer vacation." There's a short gap for schools, usually a week, when they are closed for Christmas and New Year's. When I was a kid, that was Christmas vacation. Now it is usually called "winter vacation" or something similar.