In American usage, a holiday is one day, a vacation is usually several days or weeks.
A usage that comes to mind where you don’t need an article with vacation is the expression “on vacation”.
He’s on vacation and won’t be in the office again until August 21st.
Otherwise you need an article, etc.:
- take a vacation
- a two-week vacation
- a short vacation
- my summer vacation
- the best vacation I’ve hever had
The Brits use the word holiday somewhat differently than Americans do, so that might be best described by a Brit. But I think if a Brit says “on holiday” it means the same thing as when an American says “on vacation”.