To take time off – to be absent from work, at home, or on vacation.
Ex: I’m going to take a few days off to visit my parents.

To take a vacation – to take time away from work, especially when you travel from pleasure.
Ex: I’m taking my vacation next month. We’re going to Greece.

To take a sabbatical – to take time away from work to study or travel, usually while continuing to be paid.
Ex: He’s on sabbatical while he does his MBA. He’ll be back next month.

To take unpaid leave – to have an authorized absence from work but without salary.
Ex: She’s taken some unpaid leave while she moves the house.

To be off sick – to be absent from work due to illness.
Ex: When you’re off sick, you must provide a doctor’s note.

Sick leave – the time when you can be absent from work, often while being
paid part or all of your salary.
Ex: She is having an operation and she’ll be on sick leave for the next two months.

Maternity leave – the period a mother is legally authorized to be absent from work before and after the birth of a child.
Ex: Her maternity leave finishes next week but she is not coming back to work.

Parental leave – the time that a parent is allowed to spend away from work to take care of their baby.
Ex: He has taken parental leave to look after the baby while his wife returns to work.

Statutory sick pay – the money paid by a company to an employee who
cannot work due to illness.
Ex: If you are absent from work due to illness, you may be able to claim sick pay.

A public holiday – a day when almost everybody does not have to go to work (for example in the US July 4th or January 1st).
Ex: We have 25 days paid holiday plus 10 public holidays.