typically there's a sick and vacation subset for "PTO". like you get 2 weeks vacation and a week of sick days. Sometimes they're interchangeable sometimes not. It all depends on where you work. My employer only deals in vacation days, sick days are basically "don't abuse it and we don't care" similar to your setup.
here in Germany that's the legal framework, i.e. you have a balance of vacation days (I get like 3 every month when starting a new contract, and after a year I get the whole allowance of vacation days in january).
Sick days are sick days and are not taken from that balance, I think a doctor's not is required after about 3 days of sickness, some employers demand it on the first day.
Also: With a doctor's note, you can also reclaim vacation days when you have been sick. So, suppose you took one week vacation, but you contract let's say pneumonia the week before, you get a doctor's note on your sickness, and neither go to work or on vacation but can reschedule these vacation days.
I do think its a fair system overall, employers are typically large enough to buffer the risks, and I think there is a difference between being employed and being contracted.
