"holiday" = the annual and usually paid time you get off work. In western countries, most people get at least two weeks. Example: Where did you go for your holidays last year? It also refers to those days when the law says businesses must close, e.g. Xmas Day, Easter Monday etc Example: The bank was closed when I arrived, because yesterday was a holiday.
"leave" = time when you can go away from your job. It's a word mainly used by places like the army. But for ordinary work, people may go on family leave/ compassionate leave for a funeral or sick leave. Example: He has the flu, so he is away on sick leave.