Yes, 'vacation' is an American word. The rest of the Anglosphere calls them 'holidays' (although Canada uses both terms).
'Vacation' used to be a British word, several centuries ago - which is how the Americans got hold of it. But it specifically meant a long summer break taken by the law courts & universities, because wealthy families used to vacate their main home to spend the summer at their summer residence.
In the UK, we refer to the public or religious holidays by their name or purpose (e.g. Christmas, Lent, Summer Bank Holiday or whatever) and we call any longer-term recreational break a 'holiday'. Hence my comment; to be truly British, the question should have been worded as "The last time you were sunburned, you were on holiday."