Holiday = holy day contraction. In other words, it's universal. New Year's is a holiday because it means something to everyone. Same for Christmas, a national birthday, whatever. It's also only one day. Christmas Day is a holiday, not a vacation.
A vacation is an individual thing. If I take the last week of September off, that's not because it's a holiday, it's just a vacation. It can also be a week or longer, no holiday lasts a week. You can take a vacation during a holiday, such as the week between Christmas and New Year's, but it's not a week-long holiday.
There is also the implication of travel. People travel for vacations, but for a holiday you may not (as it's just one day) and just stay home. You don't usually take a week off work and then sit at home and do nothing the whole time.
A holiday and a vacation are two totally different things with a bit of overlap.
To just use the word "holiday" for any day that's not at work is...lazy and imprecise.
The Jedi Master