The difference between 'vacation' and 'holiday'

What's the difference between 'vacation' and 'holiday'?

"Vacation" and "holiday" are words with similar meanings. They both describe days when you don't go to work or school. There are differences between them, but they can be a little difficult to discover on your own.
Holidays are for everyone

One big difference between "vacation" and "holiday" is that we use the word 'holiday' to talk about days that are celebrated by a lot of people. They include religious holidays:

• Christmas
• Rosh Hashanah
• Ramadan
• They also include national holidays. An example of a national holiday for the United States is Independence Day.

If everyone that you work with is out of work on the same day, it's not a "vacation".

Vacations often involve travel

If you tell someone about your "vacation" the conversation might go like this:
You: I took a vacation last week.
Them: Where did you go?

That's because vacations often involve traveling somewhere.
A new word that's become a bit popular in the last 10 years is "staycation". A "staycation" is a holiday that you spend at home. 
British and other English varieties.
The rules above are for American English. British English uses "holiday" in both cases:

Monday is a holiday.

I'm going on holiday next week.

What about other days?
There are some days when you don't work that are neither "holidays" nor "vacations". For example, if you stay home one day just to relax, what do you call it? It's not a general "holiday" but you're not going anywhere so it's not a "vacation" either. You can call such a situation a "day off":
I'm going to take a day off this week.

A lot of people don't work on weekends (Saturday and Sunday). To talk about those days, just call them "the weekend":
I can't wait for the weekend!

But if you have a job that requires you to work on weekends, you still have days each week when you don't work. Call those your "days off":
What are you doing on your day off?

If you're in school, you also have weeks or months when there are no classes. Those are called "breaks":
What did you do over summer break?