There are a few words and phrases used in English to describe days that you don't work.
The simplest, and most general phrase is "day off". A day off is any day you aren't working (generally, with the build-in assumption that normally you would be working that day). For example:
- Sunday is my day off this week.
- I love this job, because I work Monday through Friday; the weekend is my days off.
- I was sick, so I took a day off.
To be more specific, in English we also have "vacation day" and "sick day":
- A vacation day is any day that you would have worked, but are taking a vacation.
- A sick day is any day that you would have worked, but are sick.