In the US, a "holiday" is an established day off for the entire company. For example, Christmas Day, Memorial Day, Labor Day, etc. The entire country recognizes these days on the same day. Some companies let you have a "floating holiday" that you can take on a different day, but it counts as one of your ten paid holidays (or 5 or 12 or however many your company recognizes).
Your "vacation" pay is for the days you take off on your own, for a family vacation, a day to plant your garden, or whatever you want to do with it. Usually the number of paid vacation days you get will increase in increments as you work someplace longer. My company gives you 10 paid days of vacation for the first five years, and then you get 15 days.