In most companies it is as stated, first they take your sick days, then your vacation days.......and more and more companies are combining the two...ie PTO.
Several years ago I was bit and scratched by a cat. Without a lonnggg story suffice it to say I ended up in the hospital 4 days later. I was very fortunate, in that I had sick time, which means I was still paid. And their policy was any unused sick days at the end of the year, went into another account for more major illnesses.
At the time ,I had worked there for 3 years and used minimal sick time so I had several days in the back up account, which means I was paid for the 10 days I was in the hospital.( Praise the Lord)
They have since changed their format and use the classic PTO system.
Current job has sick days and vacation days, but you earn the days as you go so I am currently in the minus on vacation but will earn my way out. I have 57 hours in sick time....too bad it can't be used for vacaction