From my experience, most small firms are in line with what Carina has explained. I might add that vacation time is for vacation only, not carried over, and not usually for medical leave.
Personal leave days (used for family issues, mental health and/or sick days) are usually an additional 5-10 days which cannot be carried over and should be scheduled.
However, policies are guidelines and life presents extenuating circumstances. Human Resources is about caring and supporting staff who are often like family. In extenuating circumstances, I have seen firms administer policy exceptions with fairness in order to support the staff member for better “back to work” results.