Janie, odd interpretations are appearing. Holiday from the Old English as you state.
Vacation- from Old French or Latin, vacare, to be unoccupied.

UK public holidays-
14 listed, but only 6 national for the entire UK- New Year's, Good Friday, early Bank Holiday, Easter Monday but not in Scotland, Spring Bank holiday, Summer Bank Holiday (but not Scotland), Christmas Day, Boxing Day.
Others in Scotland and Northern Ireland.

U. S. Public Holidays, 10
New Years, Martin Luther King, Presidents Day, Memorial Day, Independence Day, Labor Day, Columbus Day, Veterans Day, Thanksgiving Day, Christmas Day. Emancipation Day in Dist. Columbia only.

Canada Public Holidays- only four nationally-
New Year's, Canada Day, Labour Day, Christmas Day
Boxing in federal jurisdictions and Ontario only.
Good Friday statutory, but Easter Monday in Quebec


Vacation
OED- a fixed holiday period between terms in universities and law courts.
Example- The Easter vacation.
-I tended to see them during university vacations- particularly Christmas.

North American- varied usage. Basically, a Holiday.
Examples- he took a vacation in the south of France
-People come here on vacation
- I had seen the movie in Paris while on vacation over the holidays.

Vacation, other sense-
-His marriage was the reason for the vacation of his fellowship.