Your British colleague is “on holiday”. Your American client is “on vacation”. Same beach.
Your British colleague is “on holiday”. Your American client is “on vacation”. Same beach.
German has one word for this: “Urlaub”. English has two, and which one people use depends on the English they learnt.
British English: holiday = Urlaub. American English: vacation = Urlaub.
In Global English, the English of international business, both are understood everywhere. You don’t need to choose sides.
One thing worth knowing: in British English, ‘holiday’ can also mean a public holiday (Feiertag). “I’m on holiday” means you have time off work. “It’s a holiday” means the office is closed.
Quick win: Use whichever word feels natural. Both are correct.
