There are different words for that all over Europe - in maybe 50 different languages.
In the UK we call it a holiday.
That's because in the past, people took days off work on or near the traditional holy days - Easter, Xmas, Whitsun, etc. Over the years, other days off work also became known as 'holidays'.
We don't use the word 'vacation' as that would imply, as you say, emptying a house or leaving a dwelling vacant - which very few people did/do when they go away for a week or two. In the past, the servants would remain in the property when the middle and upper classes went 'on holiday' - and they were the only ones who could afford to do so.
More recently and nowadays, other family members might well still live at the address, or they'd get in house-sitters.