We are going on a summer holiday!

Madonna sings it:

"If we took a holiday
Just some time to celebrate..."

And in Canada we go on our summer holidays.

But in the American part of the world, it's not a holiday- but rather a vacation.  You need to vacate!

If I think of it a bit further, it seems that the holiday seems to refer to a public day off, that you don't get to choose, like Labour day or Memorial Day.

Maybe that's the difference.  Time off is serious business in the US.  If you have the choice, you choose to vacate.
And if you don't have the choice and are gifted a day off, it's a holiday.

And in Canada, it's always a party whether you make it your own or take your own time off: it's a holiday!