In American English, vacation is when you deliberately take a period of time away from work or studies. This is synonymous with Commonwealth usage of the word 'holiday'. In American English, 'holiday' refers exclusively to days that religious or social groups deem significant enough to be worth observing, i.e. Christmas, Easter, Halloween. A day off is simply any day when you typically would have to go to work or school, but for some reason don't. For example, tomorrow Americans observe MLK day, so I have off Friday and Monday, they are thus, my days off. :) I hope this was helpful to you and anyone else reading. Peace!

For Americans, vacation is time that you take off from work. It does not mean that anyone else is taking vacation at the same time. A holiday is a day off from work or some celebration that large numbers of people (probably all the people in the country) recognize and observe. Christmas in western countries would be an example of a holiday. Taking a day off is a little less formal than a vacation. It usually means that you didn't plan it, but you need to take a day off work to go to the doctor or maybe that work is just too much and you need an extra day of rest.

Good question.Which I have been suffered for such a long time.lol...