'Vacation' and 'holiday'...Hmm, what's the difference?

Holidays are for everyone
In American English, 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
- Easter
- 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
In American English, 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? Let's figure out what's what.
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.
What are you doing on your day off?
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 weekrnd.
Are you doing anything nice this weekend?
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?
Grammar
"Holidays" is usually used after 'the', 'my, 'your' etc. when it refers to a single period when you are travelling or are not working or studing:
Soon it will be the holidays.
Where do you want to go for your holidays?
What are you doing in the school holidays?