"I've booked Friday off" means you've given warning (or reserved) that day in advance. It generally means you have obtained approval from your employer, so it could be both paid or unpaid. Re: a day when you are ill. If I was feeling sick at work today and was going to stay home tomorrow, I would say: "I'm going to take tomorrow off sick" or "I'm going to take a sick day tomorrow" or "I'm going to take sick leave tomorrow".

I've booked Friday off could mean either paid or unpaid leave. To refer specifically to paid leave you could say "I'm taking annual leave on Friday".

Thank you Allyson! :)

“I took Friday off” If you are taking a day off because you are sick, you are taking a sick day.