Yeah, I think you misunderstood. In Europe, "vacation" pretty much universally means "paid vacation". Otherwise, we'd call it "unpaid leave" or something.
I've only recently -- in threads here on HN in the last few weeks, in fact -- encountered the acronym "PTO", and concluded from context that it must mean "personal time off". (Right?) I also didn't quite grok what the GP meant by including those "two weeks of PTO"; WTF are those, in a European context? Can't be sick days, because AFAIK at least in most of Europe there's no quantitive limit on those: When you're sick, you're sick. Have I understood correctly that Americans who happen not to be ill for more than the "sickday limit" in a given year usually take the opportunity to "use up their sick days" even if they're healthy? (To repeat what is rapidly becoming my refrain on here: God, America is weird.)
In some companies, there is a separate "sick day" allowance, but that's rapidly vanishing. In most companies it's all put into a single bucket and your employer doesn't know or care about the reason you are not at work. It does not matter if you just want to stay at home and take care of things or fly to Venice.
If you are too sick to work for an extended time, then there is a disability insurance program. Sick days, for companies that have sick days, are for things like the flu, dental appointments in the middle of the day, etc. They are not for months-long cancer treatment.
Point being, when I go on vacation, I take PTO. There is nothing else to take if I want to be paid.
I think my company also has an unpaid leave program for unusual situations - say someone wants to take a year off to go to school but they still want their job waiting for them when they come back. But using this is very rare. Of course, each company is different as benefits are part of how firms compete for workers.
I've only recently -- in threads here on HN in the last few weeks, in fact -- encountered the acronym "PTO", and concluded from context that it must mean "personal time off". (Right?) I also didn't quite grok what the GP meant by including those "two weeks of PTO"; WTF are those, in a European context? Can't be sick days, because AFAIK at least in most of Europe there's no quantitive limit on those: When you're sick, you're sick. Have I understood correctly that Americans who happen not to be ill for more than the "sickday limit" in a given year usually take the opportunity to "use up their sick days" even if they're healthy? (To repeat what is rapidly becoming my refrain on here: God, America is weird.)