There is a difference and I hope my explanation will help you understand.
Holidays = Christmas, Thanksgiving, New Years, etc. etc.
so, if you were to take a vacation during those days or during "the week of" those days, etc. then you would be taking a "Holiday vacation".
Let's say you are going on a trip during the week of Christmas, then you would be going on a "Holiday Vacation".
If you are going on a trip that is not during a specific holiday time then you are simply "taking a vacation" or "going on vacation"
A lot of people that are learning the English language will use "I"m going on a holiday" when they actually should be saying "I'm going on a vacation". They get the two confused.
Holiday = Christmas, New Years, etc., etc.
Holidays = the time (week of) those days: Christmas, New Years, etc.
Vacation = could be during the "Holiday time" or any other time.
I am going on vacation during the Christmas holidays<--correct
I am going on vacation this summer<--correct
I am going on a holiday<----NOT correct.
I am going on a vacation<---correct
It is a little hard to explain but I hope in some way this has helped you.